Interesting 666-digit Numbers - Numberphile

Featuring Tony Padilla. See all three videos in this Apocalyptic Trilogy - bit.ly/ApocalypticTrilogy
More links & stuff in full description below ↓↓↓
The other videos in the series are:
Apocalyptic Numbers - • Apocalyptic Numbers - ...
Goliath Numbers - • Goliath & Leviathan Nu...
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...
Prime Numbers Playlist - • Prime Numbers on Numbe...
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The image of Everton FC winning the league thousands of years in the future is AI generated and not a real photo from the future.

[@numberphile]

See all videos in this trilogy at bit.ly/ApocalypticTrilogy

[@IDFpartyboi972]

Thanks for your support UK and sorry about those aid workers. I was up late the night before so I was super sleepy the day I picked those 3 targets.

[@WhataMensch]

Hey numberphile can you do a video on the number 40K? It seems relevant to current day.

[@LucenProject]

6:29 "I can talk about this all day." Plenty of people SAY that, but Brady's actually made a career out of it, and it's been a gift to the rest of us!

[@FLPhotoCatcher]

I found an interesting thing. I added the first 10 Fibonacci numbers (not counting zero) and then squared it, then divided that by 666 and got 30.70 *420* 420 *420* 420 *420* 420 *420* ...

[@shafiqeakhtar6687]

can you plz solve this link problem

[@LawrenceMclean]

The second number, ending in 1837, 18 x 37 = 666.

[@anuragjuyal7614]

Nice catch 😂

[@FLPhotoCatcher]

And 18 is 6+6+6

[@LawrenceMclean]

@@FLPhotoCatcher Indeed. All of the repeated 3 digit numbers have that characteristic, for example, 444 = 37 x 12, and 12 = 4 + 4 + 4.

[@RobertoTifi]

​@@LawrenceMcleanso I would expect 37 x 21 = 777 and 37 x 24 = 888? Wait a minute... It IS SO! 😮 37 MUST be such a devilish number, ban it out of holy places 😂😂😂

[@LawrenceMclean]

@@RobertoTifi 😀😀

[@PeterVC]

Also, that 5th Fibonacci number F3188 is the only one of those 5 that contains the sequence 666 in its digits :D

[@Cypekeh]

3188 apocalypse confirmed

[@kaerlighe9]

Hi I Am new .Could you please elaborate how the 666 fit into 3188 - and how the letter D is relevant. Thanks

[@fugcat]

​@@kaerlighe9nice try chatgpt

[@steamstories1279]

Half-Life 3 confirmed for year 3188.

[@kaerlighe9]

@@steamstories1279 could you please make an example ? Thanks

[@Senf71]

Not very surprising that there are 5 of them. For any number of digits there are between 4-6 Fibonacci numbers with that many digits. Most being 5.

[@landsgevaer]

And 6 only for 1-digit numbers if you start from 1, 1; never again after that.

[@billr3053]

4.785 approx. fibs per order of magnitude

[@chrislewis7811]

Yeah, why is it presented as some difficult problem to find these?

[@illusion-xiii]

@@chrislewis7811 I don't think it's presented as a difficult problem, I think it's presented as an interesting result. Finding them just involves doing iterative addition, easy for a program. Whether the result is truly interesting may be subjective, but its made for an engaging enough video (we're talking about it).

[@coloneldookie7222]

Agree on the rather regular 5 Fibonacci numbers in the Apocalypse set. But, what about the 666th Fibonacci set of the maximum (6) values? THAT'D be a uselessly fun superstition to make.

[@Garmasmi]

6049 in the Hebrew calendar starts in 2288 CE.

[@zeybarur]

So Everton definitely won't win the league that year

[@MichaelKrzyzaniak]

Please do talk about it all day!

[@MizardXYT]

The 23rd (23 is prime) Fibonacci prime (the 4723rd Fibonacci number, 4723 is prime) has 987 digits, which is also a Fibonacci number.

[@MaxMustermann-kf7fu]

23 -> 2/3 = 0.666...

[@quantumfoam539]

Plot twist: Maybe the release itself of so many Numberphile apocalyptic videos is the sign that the End is near

[@nathanderhake839]

I love seeing these videos with Tony. Always very interesting.

[@GoodWoIf]

I was hoping for some stuff about 616.

[@BibleBlack667]

Finally! Someone else concurs!

[@unvergebeneid]

This trilogy was a bit too base-10-based for my taste.

[@Alex_Deam]

Should've used 666 as the Number of the Base

[@dielaughing73]

@@Alex_Deam The Number of the Based* * or Baste?

[@asheep7797]

should've used base 6 and see if 666 appears (hint: we know the answer)

[@MushookieMan]

@@asheep7797 It does i found it

[@Tahgtahv]

@@asheep7797 Using 012345 is a bit arbitrary. You could use any 6 symbols you want to form your base 6 numbers, and then it might appear or might not.

[@jacksonstarky8288]

I'm not surprised that there aren't any prime 666-digit Fibonacci numbers, but I was surprised that there were five Fibonacci numbers with 666 digits... at least until I thought about how the sequence is generated and what Tony said earlier about the exponentially-increasing sample size as we increase the number of digits.

[@GayNeekOG]

Somewhere a Hollywood screen writer is salivating over this video 😂

[@fosterdawson7339]

Thank you numberphile for the 3am est upload

[@plackt]

Wait, is the third Apocalypse Prime 1....6409 (two squares), as was written, or ...6049 (only one square), as was printed?

[@RichardHolmesSyr]

It is 1...6409.

[@chrislewis7811]

4:02 what "looking for" is there here? The nth Fibonacci number is the nearest integer to phi^n/sqrt(5), so it's completely trivial to find all the Fibonacci numbers of any given length using logarithms.

[@GeorgeDCowley]

Not everyone knows that.

[@jimmyzhao2673]

These mathematical incantations are getting very dangerous.

[@wiseSYW]

3:25 that is a lot, but compared to all numbers with 666 digits, it's only 0.0059% of it

[@yanntal954]

1:44 First Turing complete computer by Charles Babbage was conceived in 1837! Maybe it's a sign that something like AI will wipe us all 😂

[@babynekochara6997]

Video suggestion: the "jump all but one" game or other similar small handheld puzzles (say 15 puzzle, but that's been done before)

[@N.I.R.A.T.I.A.S.]

"There were loads of riots in New York City, basically driven by poverty. The banks were failing as well." Me: 🤔

[@adamhanninen8295]

Personally I want to hear a deeper discussion on Tony’s latest preprint about the -1/12. 👌🏼

[@stevefrandsen7897]

If Tony could talk about it all day then I could listen all day

[@pacman52280]

I wonder what the 666th number that is both a prime number AND a Fibonacci number.

[@SangaPommike]

There's 2 apocalyptic apocalypse numbers! Who knew!

[@ubertoaster99]

Everton -2 points today. Sad times for Tony :o(

[@pedrocasella2315]

They should invent a property of apocalyptic numbers just so that 2020 fits there. This would be very meaningful...

[@ceulgai2817]

Imo, apocalypse numbers are nonce, since they're entirely dependent on your counting system.

[@frankharr9466]

That does seem like a lot of fun.

[@ecsodikas]

Why are there not 666 videos in this series?

[@doctorscoot]

Of the primes which are also Apocalypse Numbers, how many Mersenne Primes are there?

[@mugenversstudios613]

"Oh, here's to my sweet Satan. The one whose little path would make us sad, whose power is Satan. He'll give those with him 666. There was a little tool shed where he made us suffer, sad Satan." -Led Zeppelin, 1970, from a backwards recording of "Stairway To Heaven"

[@DukeBG]

Prime numbers are not that rare. I'm surprised with all of Brady's experience, he still thought they are. As Tony says, the estimation is N/ln(N), so if N has form 10^x, then pi(N) = 10^x/(x * ln(10)). The denominator is just knocking off log10(x * ln(10)) ≈ log10(x) + 0.3 digits from the numerator's power. 666 is 3-digit long, so the amount of primes would be ≈ 10^(666-3). Prime numbers are very much not a rarity at all.

[@ph1ber]

I'm pretty sure his confusion comes from this: If you pick an integer uniformly at random from the first N, then the probability of drawing a prime is 1/log N. So as N increases, you are less likely to draw a prime. So in this sense, they indeed become "rarer". You are of course correct that the number of primes between, say N and N/2 in absolute number increases as N increases.

[@minirop]

@@ph1ber and the fact, that the difference between 10^666 and 10^662 is enormous. it's not just 10^4

[@DukeBG]

Yes, exactly. But compare it, to, for example, squares. There are ridiculously less squares than primes. There would be about 10^333 with 666dd. Still a lot, of course.

[@Cerzus]

2:10 So is it ...6409 as Tony says or ...6049 as in the animation?

[@SgtSupaman]

You'll find out in the year 6049...

[@zakblackhawk204]

Thought of an interesting problem.... There are 18 4-digit numbers that contain "666", 19 if you count the one with leading zero. That's 18 out of 9000, or 19 out of 10000. For more digits, there are more that contain it, and also almost twice the percentage. So at what number of digits are there MORE numbers that contain "666" than which don't? I predict it's over 503 digits, but it might actually be less. Can't find an answer to this anywhere. A simpler parallel is for what number of digits there are more numbers that contain the single digit "1" or any other, than which doesn't....

[@edvardpiano]

You can figure out in your head if 1...(a bunch of zeroes)..1 is divisible by 11 very easily, since if the alternating sum of digits in a number is divisible by 11 the number itself also is. So 101 is not since 1-0+1 = 2 but 1001 is since 1-0+0-1 = 0 Meaning that any number with an even amount of digits starting and ending in one, with a bunch of zeroes in between, must be divisible by 11.

[@hmwndp]

I see the video was uploaded 9 minutes ago, but all the comments are from up to 1 hour ago!

[@OneBentMonkey]

Now that the series is over I hope all the paper was ritualistically burned according to the ancient rites to avoid summoning something 😂

[@alexisdespland4939]

what is the highest number that is both a fibanachi number and pr a prome nuber.

[@GreatCollapsingHrung]

Please don't change this channel to Numerologyphile

[@Chuaaaaaaaaaaaaa]

Tony has a bunker somewhere probably...

[@NyznTvfk]

u forgot to mention the magic squares of 666; 3x3 squares especially...

[@Jebez42]

I have just one word to describe the correlations made in this video - woo

[@dogwalker666]

You made this about me 😂

[@mtranchi]

3:24 10^662? So like an order of magnitude more than the amount of atoms in the universe?

[@OmnipotentPotato]

Imagine if there were an apocalypse Fibonacci prime which has 666 among its digits 😶

[@danobro]

How the hell are there comments from 1 day ago when the video is only 41 minutes old?!

[@KRAWofficial]

The video was probably unlisted

[@asheep7797]

It was unlisted, but people could access it via the description in the first video.

[@yoram_snir]

Wonderful 💎 I can listen to that stuff all day

[@MrAmalasan]

felt like you were battling the focus a lot in this trilogy, disorienting when going down to the paper

[@Bear-re5xm]

Is there any sequence of X length fibonocci numbers greater than 5?

[@telhudson863]

x=1; 1 1 2 3 5 8. That's the only one.

[@tamirleibovich]

Just opened my bank account and I’m quite far from a 666 digit number

[@sherriffs2554]

You should have probably noted that π is just a denotation here and not a value.

[@shannonmarbut3648]

I think if you try hard enough, any number can be expressed as a power of 666. It won't be a whole number power though

[@emuhast]

Looking at the soccer-robot picture and remembering the "Legions" in the last video, i have to ask: Did you use AI to make those images?

[@aryst0krat]

Pretty clearly yes, I'd say.

[@davidfraser2946]

up the toffees!

[@damyankuzmic5605]

Hi hello howdy with greetings bless

[@danobro]

Imagine getting the 666th like - what an honour that would be

[@steveclark2205]

666= All numbers on a roulette table added together ❤️

[@TonyManso]

Has anyone tried dividing F3188 by F3187 of the fibonacci sequence?

[@skyscraperfan]

I read "apologetic" number 😀

[@franckplanks]

As of April 23, 2024, this channel has reached 666 million views.

[@MrBeezweeky]

How many numbers are 666 digits long

[@msolec2000]

9*10^665

[@PeterFreese]

What is the probability that a Fibonacci number is a prime?

[@Sara-zr4yz]

Just for fun, are there any prime numbers like 999888777666555444333222111 or 999997777788888666664444422222255555111113333333 ? Just curious.

[@kiro9291]

"maybe these are years. :)"

[@DjynnFlyssa]

This trilogy's been great fun, but it's a shame to see so much machine-made imagery. The illustrations bring so much character to the videos, and seeing that farmed out to "AI" is sad!

[@Evil_Narwhal]

What part do you think is using AI?

[@DjynnFlyssa]

@@Evil_Narwhal The 6049 football team in this video, the images of demons and giants in the previous two.

[@stevehines7520]

time signature: 6:55

[@madansaini8184]

Satte ke number kaise nikale iski uski nikaalne ki calculation

[@shruggzdastr8-facedclown]

What about alpaca lips numbers? 😏

[@TheCosmicGuy0111]

Woah

[@romanvolotov]

they did everton dirty

[@scottsinner7530]

I’m sorry, in what world did Everton win the league in 1995?

[@Euler13]

He didn't say they won the league, he said it was the last time they won anything. They beat Manchester United in the FA Cup final.

[@znotch87]

All day, but only 6 minutes? Damn shame!

[@WallyST675]

Had to hit the like button for the 667th like, sorry about that.

[@VikingTeddy]

I hate that we can't downvite anymore. It's 667 for goodness sake!

[@johnbones261]

Queen Victoria ascended to the throne in 1887?.

[@joemroz1033]

1837

[@unyous3319]

SIR SHILONG SATTA GAME FR KA NUMBAR SINGLE DIJIYE EVERY DAY THSNK YOU 🎉.

[@shruggzdastr8-facedclown]

6049 will be the year when the Cleveland Browns will finally win a Super Bowl! 😏

[@sayeager5559]

6094. The 60th day of 1994 which is March 1. Justin Beiber was born......

[@primarykeymusic]

6049 or 6409?

[@kalmdwn7711]

while in other cultures it's triple luck

[@Gabelolguy]

Should've done this one on Halloween, boys. That's a scary scary base

[@PlasteredDragon]

The thing is that all "special" numbers based on digit patterns immediately lose their "specialness" if you look at them in any base other than 10. So really we're just exploring things that are curiosities of base 10 rather than things that are special about any of these particular numbers. Pick a number N that is special because of digit pattern X in base 10. I'd be willing to bet that N-1 while not special in base 10, is probably special with digit pattern X in some other base. Same for N+1. I dunno it just feels akin to changing your printer ink cartridge and then getting excited about the new "DARK" numbers that come out afterward.

[@stevehines7520]

19

[@undr3s1]

this is some devil's number

[@user-ge9ed9km4k]

こんにちは😃😂😊❤

[@RobertMStahl]

666, 6

[@TheDarkElder]

Just 5 of them. Literally a handful. That must be the sign we got five fingers. I smell a conspiracy! 😀

[@JohnPretty1]

Mathematics + Superstition = Physics. QED

[@scoon2117]

666

[@user-ed4kp3lt2m]

We need translate to Arabic with thanks..

[@user-fd3qq6cj2v]

X^3=2X=X+X

[@user-fd3qq6cj2v]

Root 2, cube it, divide by 2. Ad infinitum

[@robertolson7304]

How do you even measure 3 locations to find slope? What would take you to measure 3 locations find a slope? Rise, run, and ?. Rise,run, width? Then put that into 3 locations. 3x3=9. That has to equal .666 or 666.0.... idea is you have 6 happening 3 times. So 3 locations of 6 value.

[@andreysmirnov5482]

First!

[@davidmaxwaterman]

Something bothers me about calling them "Apocalyptic"...some cultures would consider it very lucky.

[@brucea9871]

A rather uninteresting video about "interesting" 666 digit numbers. There is nothing inherently interesting about 666 digit numbers. I think this unjustified fascination some people have with the number 666 is due to a Biblical reference to it. From my understanding the number 666 is used in the Bible only as a coded reference to a particular king (or some other ruler) the writer was criticizing. To avoid possible punishment the writer referred to the king using a code (which happened to produce the number 666) his followers would understand but the authorities would have difficulty proving his use of 666 was actually a reference to the king. An even more useless aspect of your video was referring to incidents that happened in the years represented by the final four digits of particular 666 digit numbers. The only meaningful part of your video was the reference to Fibanocci numbers since as you pointed out they do seem to occur in nature.

[@VoidHugger]

WHY are you using AI. Why. This channel used to have such beautiful art sometimes, now its AI slop

[@seanmay9181]

Stop doing the jerky cam with random zooms in and out. This isn't the nineties.

[@MeriaDuck]

Go watch something else then. This isn't the nineties with only a handful of channels.

[@danamulter]

2:30 : you can afford to pay a real human artist to do real human art. This bot trash doesn't belong in my feed or not labeled as "containing AI generated content"

[@landsgevaer]

If there can be computer-generated numbers in there, and mathematicians use computers, instead of paying humans to calculate 2^666 by hand, then why not computer-generated art, when artists also use AI? It is just a tool.

[@danamulter]

@@landsgevaer Because, you deliberately-misconstruing knuckledragger, one thing is a tedious repetitive task and the other is a career in reflecting the human condition in realistic and fantastic ways. This is saying "Our HUGE channel thinks a few prompts is worth the same market space and validity as "art" as a human creation". It's scummy, and your absolute lack of capacity to comprehend this speaks far more than you could ever know.