Apocalyptic Numbers - Numberphile

Featuring Tony Padilla. See all three videos in this Apocalyptic Trilogy - bit.ly/ApocalypticTrilogy
More links & stuff in full description below ↓↓↓
The two sequels to this video are:
Goliath Numbers - • Goliath & Leviathan Nu...
Primes and Fibonacci with 666 digits - • Interesting 666-digit ...
Tony Padilla on Amazon - amzn.to/3U6DRSM
(Check out “Fantastic Numbers and Where to Find Them”)
See our 666 Playlist - • 666 on Numberphile
Big Numbers Playlist - • Big Numbers on Numberp...
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[@numberphile]

See all three videos in this Apocalyptic Trilogy - bit.ly/ApocalypticTrilogy

[@alanzyoutube]

These big number videos with Tony are the best ones, We need a video of something like Graham's number, Tree 3, Gama Zero, Arrow, Factorial & Rayo's number. G↑ x T3↑ x Γ0↑ x ↑ (number of arrows is ↑) x ! (number of Factorials is !) x R↑ + 1 = Big Daddy Number!

[@Defnotyeett]

Hey, why do youtube views stop at 301? (ps: check the video)

[@IDFpartyboi972]

Much love from the IDF numberphile

[@ppchan9516]

geometry dash

[@johnjeffreys6440]

The closest explanation I have found to explain why 666 is the number of the beast, is that it's symbolic of materialism. The carbon atom has 6 protons, 6 neutrons, and 6 electrons.

[@liliwheeler2204]

Any time I start to think I have a grasp on exponential growth, I see something like 2^157 Planck times = a few hours and 2^192 Planck times = 10 million years, and it breaks my brain again

[@jamesknapp64]

Well it's 2^35 times bigger, 2^10 ~ 1000 Thus 2^35 > 32000000000 times bigger or 32 Billion times more

[@THICCTHICCTHICC]

Consider it this way - 2^10 is damn near 0 compared to 2^11 and so on. In the same way that the difference between a million and a billion is pretty much just a billion.

[@arcuscotangens]

I love hat animation. Implying that the last living creature in the universe doesn't die because of cosmic events destroying galaxies at a time, but simply because it's a bit clumsy.

[@mudmug1]

Stumbled just shy of reaching the peak of Mount Improbable

[@publiconions6313]

Ill never forget watching Brady's interview with Conway - when Conway looks out the window and asks "i wish i knew whyyyyy".. in reference to the strange universe-implicating numbers in group theory.. why the monster and no more, why any of the sporadics at all... especially when we know symmetry has so much to do with fundamental physics. I love hearing Tony say "hey im nature, that's got something to do with me!"...

[@jeffspaulding9834]

RIP Conway. One of the few mathematicians that I've directly applied their work (Conway invented the current system for naming polygons).

[@GarryDumblowski]

@@jeffspaulding9834 Wait, really? I'd have assumed it was way older, considering how long people have been doing math with higher order polygons like the constructions of the 17-gon and 257-gon.

[@jeffspaulding9834]

@@GarryDumblowski Well, it's sort of true and sort of not. People were naming polygons long before Conway, but the rules for doing so weren't consistent or well defined. Conway worked with someone named Antreas Hatzipolakis and took existing practices and codified them into one coherent system. Unfortunately, they posted it on a website that has since removed the page. I couldn't find a copy of it when I did a cursory search. Related, Conway also created the system we use for polyhedra. Wikipedia has a page for that one.

[@GarryDumblowski]

Ahh, I guess that checks out. Reminds me a lot of how long it took pi to get a consistent symbol.

[@babilon6097]

It's math. We try things. Sometimes they're even useful.

[@orang1921]

"I discovered this new property of ___. Oh, it turned out to be useful in some industry? Yeah... yeah, I meant to do that."

[@DaveLeCompte]

@13:53 Will there not be a number where the expansion is all fours? 2^2 = 4 QED

[@sh1sh1maru]

New Tony Padilla video? Count me in! Is that a goat's head on his sweater? Fitting!

[@FLPhotoCatcher]

There was a Veritasium video that showed that the number that most people give for a random number is *37.* 6+6+6=18. 18x37=666 And 37 is the largest prime factor of 666

[@martinchamberlin3359]

it's the logo for AllSaints

[@shortsornothing4981]

No. Allen solly.

[@stevefrandsen7897]

I enjoy Tony's presentations. @8:00 "Maybe this is where the last creature dies... Or it might have nothing to do with anything". Love the humility. Humility is a good trait to have for learning.

[@atalbrecht]

The animations of the creature were so adorable! Thanks for the vid Brady!

[@harmanpreetsingh7848]

Always happy to see Prof. Tony Padilla

[@Luper1billion]

I feel like all of mathematics was founded on mathematicians just playing games with numbers

[@cooltaylor1015]

Well,, before they invented numbers, they were playing games with compass and straightedge, but yeah. Basically.

[@jonathandevries2828]

strange optical illusion @4:18, the background changes from a pattern to flat brown when the numbers are scrolling up it

[@john-vincentsaddic6335]

Ah I see why! if you pause it, the numbers have a solid brown background to them!

[@kiro9291]

never have I felt so much emotion upon seeing a blue three-eyed creature

[@ismailshtewi8560]

i love little, arbitrary mathematical questions like this that don't have any seemingly important application or anything, it's just people playing with numbers and seeing fun things pop up and running with it. you could use this sort of thing to write stories or create mythologies.

[@unvergebeneid]

"Apocalyptic Powers" sounds like the better video title than "Apocalyptic Numbers".

[@video83046]

Too clickbaity for this type of channel and it's seriousness towards the topics chosen I guess

[@unvergebeneid]

@@video83046 why is it clickbait if it's literally the name of those numbers?

[@soupisfornoobs4081]

It's numberphile, not powerphile

[@drenz1523]

​@@soupisfornoobs4081 new channel: powerphile, a channel dedicated to powers?

[@davidgould9431]

Brady's comment about a power of two being all 4s was initially intriguing, but I think it's fairly easy to see why a power of 2 greater than 2 cannot be all 4s: the previous one would be all 2s and the one before that would be all 1s, which is odd and clearly not a power of 2. Edit: I should have said (instead of "a power of 2 greater than 2") something like "a power greater than 2 of 2" or, better I think, "2ⁿ, where n > 2". I appear to have caused some confusion and debate. Sorry, everyone. @hectorbector11 put it better (I summarise): 2ⁿ = 4444…4444 ⇒ 2ⁿ⁻¹ = 2222…2222 ⇒ 2ⁿ⁻² = 1111…1111 which is odd, so not 2ⁿ for any n > 2.

[@rjtimmerman2861]

What about 2^2 boom gotcha

[@Henrix1998]

22^2 isn't 444 for example, I think your logic is flawed. Btw, √444444 is 666.666. For every 2n amount of 4s the result is n.n 6s.

[@hectorbector11]

@@Henrix1998 By previous power of two he means 2^(n-1). When you go down one power in this way, you are dividing by the base, 2 in this case. 4444/2=2222. So the hypothetical power of 2^n = all 4s requires a 2^(n-1) = all 2s and 2^(n-2) = all 1s. This last one is clearly impossible, because there are no odd powers of 2.

[@lunardoesmusic]

@@hectorbector11 Well, no odd powers other than the trivial 2^0, which makes 2^2 the only power of 2 whose digits are all 4s.

[@davidgould9431]

@@rjtimmerman2861 I said "a power of 2 greater than 2." Now (knowledge bomb coming up), 2 isn't greater than 2. What was it? Boom, gotcha. Was that it?

[@rosiefay7283]

2:33 Such is his obsession with repeated 6s, he is interested in the decimal expansion of 2^192 ... but passes over the 4444 in that very same expansion.

[@GarryDumblowski]

Now you could ask the same question but with 4444 and call them Powers of Death instead (because 4 is often associated with death)

[@samuraisecretary]

"Seconds are arbitrary, let's use something fundamental" *exclusively uses base-10*

[@ShivanshSharma]

Come for the maths, stay for the existential dread.

[@t.kersten7695]

many years ago there existed T-Shirts with funny memes aorund the "number of the beast" - with prints like "667 - the neighbour of the beast", or "333 - half evil"

[@KevFrost]

What do you get if you dial 666 in the UK? An upside down policeman

[@evangonzalez2245]

668 is the neighbor of the beast, 667 is across the street 😉

[@GarryDumblowski]

As soon as I saw the premise of the video my brain immediately jumped to "so is 0.248163264128256512102420488192... normal?", which I'd argue is a pretty good reason for doing silly math like this.

[@FirHydrntsRFirEaters]

"Let's use planck times since they're fundamental to the universe and not human centric" Proceeds to discuss 666 appearing in base 10 numbers, which are very human centric lol

[@Anon282828]

"all 4s" divided by 2 is "all 2s", and "all 2s" divided by to is "all 1s" - an odd number larger than one cannot be a power of 2, so therefore there is not power of 2 that results in "all 4s" QED

[@Deus_Almighty]

2² = 4

[@LittlePunnkk]

legends say Brady will never stop giving certain numbers groups with cool new names, and then asking professors about them

[@jacksonstarky8288]

Speaking of Planck time... a short series on Sixty Symbols about the Planck units, giving each unit its own video, would be fun to see. Especially if Tony is up for doing the whole series with Brady.

[@02_aldebaranrahmanadhitya95]

Excited to watch!!

[@OmateYayami]

I wonder how they check if number has 666 for super large powers. I thought that there is some trick with binary conversion and modulo operations but 2^n in binary is like 10^n in decimal, so base changes a lot in the digit composition. It would be interesting in seeing some relations between number base, exponent base and exponent power.

[@t.kersten7695]

something like 666 to the 666th power maybe?

[@ulob]

That death of the last creature in the universe animation in the middle of the video 😂😂😂 what a gem

[@ulob]

Whaaaaat? It didn't actually perish

[@sarahmcleary4603]

I love this channel but often I get about 4 mins in before it’s over my head. This one I followed the conversation all the way through! Go me! However now I’m thinking about my relative insignificance in the universe.

[@Qbe_Root]

Hexakosioihexekontahexaphobes in shambles

[@BytebroUK]

One 6th-form teacher (whom I shall adore forever for their attitude) told me "Maths is what people think is useful, but at the same time Number Theory is what people think is interesting" :)

[@krokkoguy]

There is a very natural topic to talk about that continues some of the ideas discussed in this video, in p-adic numbers, where large powers of numbers in a sense converges to a sequence of digits

[@orphanedsignal]

thank you yet again!

[@ynes6658]

A power of two cannot be made only of sixes as it would be divisible by three.

[@ynes6658]

A number of the form aaaaaaa in base B is expressed as a×(B^n - 1)÷(B - 1), so, to be a power of two, a needs to be a power of two and B^n = 1 + 2^m × (B - 1) for some m.

[@orterves]

4:26 "I don't like using seconds because seconds are a bit man made" - uses base 10

[@Flinsyflonsy]

Proof that we should use base 3, the holy trinity, since they would have no apocalyptic numbers.

[@Nerdnumberone]

They use powers or 2 and a base 10 number system to look for 666. That's so very arbitrary. If this was some divinely inspired number handed to humans in our number system, it could be given in any convenient units. Seconds would be unlikely, as they are a relatively recent invention (within the last 500 years). Personally, I'm an atheist, so I don't believe that an iron-age book contains particular insight into the future.

[@orterves]

@@Flinsyflonsy and here I was thinking we should use base 7 to maximise the frequency

[@Flinsyflonsy]

@@orterves we can use unary and use 6 as the only digit.

[@PC_Simo]

14:00 Well, it can’t be all 4:s (other, than 4, itself, obviously); because that one will have a factor, whose expansion is all 1:s, which is an odd number; and therefore, definitely, not a power of 2 (again, except 1, itself, which is 2^0).

[@jacksonstarky8288]

A question for Tony: How far past the black hole era (statistically) would the universe have to go in order to experience a Poincaré recurrence (assuming that such things are possible; this would make another interesting video topic for this channel as well) in terms of these apocalyptic numbers?

[@jimnewton4534]

Serious (not mocking) question. In UK do you pronounce 6th as sixth or as sisth or as sikth or as siss. When the speaker says "666th" I didn't hear the siksth. Is it going out of fashion to pronounce the k in sixth?

[@KevFrost]

Regional variation. We have someone with a mostly Liverpool accent and an ?Australian? New Zealander. I do sick-zth

[@mischa7406]

I ran some code and checked what the highest n was for p^n where p is every prime below 100, and n = 1-100,000. No other p has a larger n than 2. The larger p gets, the smaller max n becomes. The sums with the highest n all seem to average around 8300 digits in length, so I suppose that around that number of digits the chance that any random combination of p and n will contain three 6's consecutively approaches 100%

[@geekjokes8458]

i didnt understand the 2nd paragraph, what do you mean by the sums? are you adding the powers of p up to a "max n"? isnt it arbitrary? and summing is not what they're doing in the video anyway... "around 8300" just seems to be the point at which your computer gave up, and i also dont se how _that_ means the number should have the string 666

[@LordElijah]

Today was my 666th day doing duolingo...

[@piemaster310]

Maybe 2^29784 is when quantum fluctuations cause the matter in the universe self-assemble into a big bang situation

[@dyerseve3001]

"Stand back, I have powers... apocalyptic powers!" Holds out a long strip of paper.

[@_lalapop]

for interesting far future shenanigans regarding the apocalypse, the last question by isaac asimov is pretty interesting

[@sumarexl]

666 is the number of the Sun. 108 is the number of the Moon.

[@PhilbertDeZwart]

We can disprove Brady's idea about a power of 2 containing only 4's by looking at the last 2 digits. There are only a few combinations that occur in a fixed sequence and none of them are 44

[@Henrix1998]

I decided to fire up Python and check what is the largest power of 2 that does not contain all N digit numbers in it. Preliminary results are the following 2^169 onwards contain numbers 0-9 2^3500 onwards contain numbers 10-99 2^53993 onwards contain numbers 100-999 (maybe) After that checking gets veery slow and I need to multithread the search properly

[@nadionmediagroup]

That final Planck number is almost irrelevant due to the vast size of the number. It’s hard to even comprehend.

[@AsterothPrime]

Belphegor's Prime

[@numberphile]

Not today - but we’ve done that before - kzbin.info/www/bejne/sJzCgmyvlLGBsMk

[@jimmyzhao2673]

This would be a good video during Halloween.

[@user-rh6ut1uc6s]

What about negative powers of 2, and looking for 666 in their decimal expansion after the decimal point?

[@NickCombs]

I'd hypothesize that the prevalence of nonapocalyptic numbers only approach zero as a limit as they get larger.

[@SgtSupaman]

You mean the prevalence of NON-apocalyptic powers of two approaches zero. The prevalence of the apocalyptic ones is clearly growing larger since it is thought all after 2^29784 might be apocalyptic.

[@NickCombs]

@@SgtSupaman yes, thank you

[@stevemonkey6666]

Tony Padilla always provides a fun video 👍

[@wv1seahawks]

I think something similarly interesting is there’s gotta be a point where every power of 2^n after a certain value of n contains the number n in its digits. That’s the one I want to know lol

[@rudolfglaser9664]

Is there actually also a 2 to the power of n number that contains the digit '6' four or more times in a row?

[@danielw.4876]

My favorite part about 666 is that it is the 36th triangle number… 36, 3 6’s And triangles have 3 angles, 60 degrees each if it’s equilateral

[@themasterofthemansion3809]

Not to mention that sum of all integers up to 36 is 666.

[@daviddoran1682]

Would love to hear more about the Vacumm of space collapsing and the Higgs becoming unstable. Is there any clues as to how the universe might become "interesting" again after all the black hole shave radiated away?

[@OrangeDrink]

Great info on history 616 or 666 depending on source! Playing math with 7 is fun too

[@cloudbaserapture99942]

Their are 216 primary colors on your screen monitor. It's called the web safe color palette. 6x6x6 = 216 = Plato's republic.

[@illesizs]

How come *seconds* aren't allowed, but *base 10* is?

[@RobLarsen]

Everything about this one is great

[@StefanReich]

Powers of 2 that contain "666"? That is not even math, just completely useless

[@Insanit13s]

Interesting video, but I have questions. How long would the 666th Apocalyptic number be in years? Do any of the Apocalyptic numbers, converted from Plank time to years, end up being x10^666 years long?

[@Snefens34]

What about numbers in the sequence 2^n that contains n? At first they will obviously be a lot more frequent compared to when just looking for 666's. A quick check gives n=(6,10,35,36,37,44,49,51, 60,67,72,73,82,85,89,93) that is true for n666 the frequency should be lower. Would that at one point also reach a value n where all following values would contain n?

[@BernardoMartins_]

They spoke of 616 as the alternative and perhaps actual number of the beast. Planck’s length, the smallest possible distance in the fabric of reality, is 1.616 x 10^(-35) m. There you have it. Everything that has a size is fundamentally apocalyptic.

[@aodtoxic]

Why not calculate the probability of a random occurrence of 666 in a sequence of random numbers. It will be possible to estimate the probability of if a large sequence exists with no 666 in it.

[@JavierSalcedoC]

Id love to see all the 1000 3 digit combination last "pure power" and see the variation

[@drgetwrekt869]

the best one is the golden ratio: phi = cos(666) - sin(6*6*6) or something like this. amazing

[@geekjokes8458]

its just sin(666°)

[@drgetwrekt869]

@@geekjokes8458 there are various versions. its funny as heck

[@SubtleForces]

To get all 4s with the n-th power of 2, the n-2nd power would have to be all 1s and there can not be a 1 as the last digit in powers of two, so the answer to Brady's question is that it can't be done with 2 as a seed. But it feels like my argument could be generalized to exclude a whole lot of seeds and a whole lot of outcomes for each seed. I wonder what the Tony Padilla could be doing with that...

[@jonathandevries2828]

i just KNOW brady is gunna ask, but are there other "apocalyptic" powers for other triplicate numbers, like 333 or 555?

[@insertcreativenamehere492]

theoretically you could find a power of two that contains any string of digits, if you go big enough (although this isn’t proven)

[@veggiet2009]

Be interesting to see 2^n where n occurs in the string of digits

[@TheCerebralOne]

you should do a video with Underwood Dudley on crank pseudomathematics

[@petrospaulos7736]

I guess he should mention how far has the search gone. This would help people to continue the search...

[@schitlipz]

By choosing Planck's time, wouldn't a more natural base also seem more fitting?

[@martinh2783]

Next morings newpaper front page: Famous mathematician Tony Padilla says: "It's Maths, who cares!"

[@lionbryce10101]

There's also the base. The prime you're using, the power, and the base you're in

[@JefferyMewtamer]

By analogy, can we call 2^24 = 16,777,216 a Holy Power since it includes the number of triple perfection to 666's triple imperfection?

[@jamesknapp64]

I was thinking if the density of powers went to 1 (the proportion of the powers that give apovolypic numbers) and it seems like something stronger is believed.

[@idonotcomplyrevolution]

666 itself isnt an apocalyptic number on its own, but is part of a sequence, such as: 111, 555, 666, 888 etc. will always sum either 3, 6 or 9. which we call tesla numbers or sometimes referred to as God's numbers.

[@Matthew-bu7fg]

I was in high school from 2005 to 2010 and I remember the rumours that the world would end on 6th June 2006. What memories.

[@GeorgeDCowley]

In Medaka Box, Ajimu Najimi has some large numbers associated with her. Are they mathematically important, or just button mashes?

[@adamsmith7885]

Revelation 13:18 18 This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666.

[@GeorgeDCowley]

@@adamsmith7885 This would be fine as a comment on the video, but has little relation to my comment.

[@unvergebeneid]

5:41 you go to all these lengths to have a unit of time that's not man-made but then you apply it to something that relies on base 10. Let alone a book written by people of course.

[@dianamelamet]

That's what I was thinking! Someone talking about numbers wants a "natural" unit. Ha!

[@JT-xh9ev]

I think he just translated it into second. Since plank time is fixed you would know exactly how many fit in a second so it would me the same time wise just an easier number for people to understand

[@patrickramos1748]

Planck time isn't reliant on base 10, it's just a measure of time, the lowest measure of time. It's just equivalent te a certain number of seconds

[@TimmehTRP]

@@patrickramos1748 But whether a power is apocalyptic is base 10 reliant. So the transformation to time is not the problem, it's the source itself. Maybe we should use base 666 :P

[@unvergebeneid]

@@patrickramos1748 exactly. But a sequence of 6s is.

[@cooltaylor1015]

I conjecture that there are both infinitely many apocalyptic powers of two AND infinitely many non-apocalyptic powers of two.

[@RUBBER_BULLET]

Reflections of my Walkman still staring back at me.

[@nopetuber]

You can't have a power 2^n made of only 6s because then 2^n-1 would be half, so made of only 3s, which would be an odd number (impossible)

[@alanzyoutube]

These big number videos with Tony are the best ones, We need a video of something like Graham's number, Tree 3, Gama Zero, Arrow, Factorial & Rayo's number. G↑ x T3↑ x Γ0↑ x ↑ (number of arrows is ↑) x ! (number of Factorials is !) x R↑ + 1 = Big Daddy Number!

[@TheOwlman]

25.806975801127880315188420605149 the root of all evil, one of my favourites among so many 666 related jokes, though 664 the neighbour of the beast (at least generally in the UK) comes a close second.

[@Decimaster321]

How big are these if they are Planck volumes?

[@xyz.ijk.]

Well, that was cheery. Can we go back to son of tree or something like that?

[@rosiefay7283]

A more interesting question: which is the largest power of 2 which is *not* apocalyptic, and what is its decimal expansion?

[@numberphile]

We explored that in the video right?

[@rosiefay7283]

@@numberphile OK, I concede the point. I admit I lost interest after all that discussion of various multiples of the Planck time interval.

[@AgentM124]

If something so "small" as 2^⁶⁶⁶ planck times already breaks any concept of time in our universe. 2^(busy beavers n) planck times is even more absurd

[@Addonski]

As a person who lives 3 hours after this video released, i can confirm that this is not the end of this world.

[@RowanAckerman]

I feel like relying on base 10 means that using the Plank time isn't useful.

[@My-Say]

What about a way to determine if reality is simulated? And then we would be faced with the philosophical question, would knowing it is true, would it devalue life? A simply string of three sixes appearing in any large number is not amazing at all. And if pi never ends, there must also be a string of 666 sixes somewhere.

[@miraadi97]

Reported for predicting when KZbin is dying. 😂

[@AdrenalineEuphoria]

Doesn't this all apply only to base 10?

[@EternalLoveAnkh]

How ironic... I just watched "Knock at the Cabin" last night, which is about the apocalypse. RJ

[@FlesHBoX]

wtf, I was taking some measurements yesterday for a thing I was designing and they added up to 666, and now today you guys put out a video starting out talking about 666... The world is coming to an END!!!

[@Forriedude]

I think it would be fairly simple to prove that a power of 2 can't be all 1 number. Every power of 2 is double the previous. So to get all 4s, the previous would half to be all 2s, and the one before that all 1s. Odd numbers aren't possible. Am I correct in that, or are my recreational maths not mathing?

[@gcewing]

1.3*10^8195 years later, the Saviour comes back and says "...Where is everyone?"

[@noclafcz]

It is 200 years after the last nuclear war and we are writing the year 210 After Brady, Holy Founder of the Apocalyptic branch of mathematics!

[@dxutube]

Is there a pandigital exponent that is Apocalyptic?