MegaFavNumbers - The Even Amicable Numbers Conjecture
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- Опубликовано: 18 авг 2020
- This video is part of the MegaFavNumbers project. Maths RUclipsrs have come together to make videos about their favourite numbers bigger than one million, which we are calling #MegaFavNumbers.
We want *you*, the viewers, to join in! Make your own video about your favourite mega-number. You can think of a cool big number, or think of a cool topic first and hang a mega-number on it.
Upload your videos to RUclips with the hashtag #MegaFavNumbers and with MegaFavNumbers in the title, and your video will be added to the megafavnumbers playlist.
Submit your videos anytime before Wednesday 2nd September to be added to the MegaFavNumbers playlist!
MegaFavNumbers Playlist: • MegaFavNumbers
Amicable Numbers on Wikipedia:
en.wikipedia.org/wiki/Amicabl...
Here is a list of amicable numbers:
www.vaxasoftware.com/doc_eduen...
A list of sums of amicable numbers
oeis.org/A180164
Remember, a test for divisibility by 9 is to add all the digits of the number together, and to do the same with the result, until you get a single digit. If the end result is 9 then the original number was a multiple of 9.
Here is a list of even amicable numbers whose sum is not divisible by 9 oeis.org/A291550
And here are those complicated mathematical conditions
www.ams.org/journals/mcom/196...
« And then Euler comes along. He finds like 60 more, 'cause that's what Euler does »
'We are like worms fighting an eagle'
What*
ruclips.net/video/TEh_4LQkkHU/видео.html
Euler : Amicable number
'Oiler', was he the greatest mathematician who ever lived?
My favorite new math quote
James Grime and talking enthusiastically about a cool number, name a better duo.
The numbers 220 and 284
tony padilla and big numbers
Cliff Stoll and talking enthusiastically about Klein bottles.
Dr. James Grime and _______ talking enthusiastically about cool numbers. Or my fav:
Dr. James Grime and Brian Brushwood marrying the words of Maths and Magic in a way that honors the memory of Martin Gardner.
Fubini and Tonelli?
1:42 "Cause that's what Euler does" :D
Hmmmm, so you're telling me that the 503rd pair breaks it? 🤔🤔
While the sum of the first pair is 504? Hmmmm 🤔🤔🤔🤔
Coincidence? Yes.
Probably. But there is an actual result called Monstrous Moonshine where a more tenuous connection between two numbers turned out not to be a coincidence.
@@grahamward4556 elliptic curves are VERY related to group theory via number theory
@@grahamward4556 there is a neet 3b1b video about it.
Holc Tomaž ah, which ones that?
@@naunidhdua the newest one also in the #magafavnumers
We're really fortunate to have a person like James Grime. Intelligent, enthusiastic about his subject, happy just to share his knowledge, super well-spoken. Good to have around!
I've always been partial to Belphegor's Prime. 1000000000000066600000000000001 is very raw.
OMG it's beautiful
@Simon Read It has bad breath.
Oh my Belzebu, I didn't know about that.
@@zethayn it is, isn't it? Man, I loved it.
Pause at the right moment immediately after 2:06 for nightmare fuel
Wow!
Came down here just to comment this, seems you beat me to it.
3816547290, uses every digit exactly once and number made of first N digits is divisible by N
...That works with any set of the 10 digits, as long as you put the 0 last?
like, 1234567890 is divisible by 10, 9876543210 is divisible by 10, etc. Am I missing something?
@@mambodog5322 if you take just the first let's say 7 digits (so the number 3816547) is divisible by 7, and that works for any N first digits
@@pocarski Yeah, I understand how it's hard if you choose anything other than 10, but I was pointing out how in the case for 10, (in the original comment) it's trivial.
@@mambodog5322 In the case for 9 it's also trivial, since the sum of everything from 1 to 9 is divisible by 9
@@mambodog5322 There are several other constraints:
- digit "5" must be in 5th position since "0" is already forced in last position.
- all even digits must be in even positions because an even can't divide an odd, and this forces all odd digits in odd positions.
- the three-digit number in positions 6 through 8 must be a multiple of 8, since position 6 is even, the two-digit number in positions 7 and 8 must be a multiple of 8 with position 7 odd but not "5", so it is one of "16
", "32", "72", "96".
- the two-digit number in positions 3 and 4 must be a multiple of 4, with position 3 odd, so position 4 must be digit "2" or "6"
and is forced by which is in position 8.
- all three-digit numbers in positions 1 through 3, 4 through 6, and 7 through 9 must be multiples of 3.
- first seven digits must be a multiple of 7.
When you factor in all those constraints, 3816547290 is the only number that works.
Amicable numbers was one of the first videos on Numberphile back in the days!
It was! I learnt this fact after making that video and have been waiting years for the right time to tell people about it.
Very nice James! :3
I wonder why he didn't give a heart to you.
@Adam Romanov stay mad lmao
@Adam Romanov You seem like a fresh toadwalker fan
While yall be beefing i be wondering how he posted this 5 days ago
@Adam Romanov bruh...
Your energy is contagious
My Little Singing Banana: Friendship Is Mathematic
4:48 James transcends all known amicable numbers and enters the hyper realm
Those numbers are very aesthetically pleasing.
*3blue1brown, standup maths, singing banana, and Numberphile* posts video on the same day!
*Legend*
Edit: Oh, so it’s about favourite numbers! Interesting...
also Tom Rocks Maths
Favourite numbers > 1000000 *
*show less Hell, don't show me any dumb comment if it's a tryhard clever wannabe funny quirky comediant shit spam. YT comments are like a comedy tryouts
I'm sad that Vihart, Matt Parker, and mathologer were not among the original videos released in this series. Them, you, and 3blue1brown are my favorite math RUclipsrs.
Matt is part of it, just a few hours late. The others have lockdown problems.
I have never heard someone who makes you like numbers like this guy.
What a fun collaboration! I hope you have lots of viewers joining in on the fun.
Great idea! Off the top of my head, my favorite large number is Graham’s number (but I suspect it is on everyone’s list!).
Pensively fanciful. A joyful bit of exploring and wondering for us, the appreciative viewers.
WOOHOOO JAMES FINALLY GETTING YOUNGER!!
You know that some redditor will try and make a vid about 6,969,696
_don't_
........
**NICE!**
I'm sorry, it's stronger than me
But the 6 on the end is lonely
Don't forget 5,318,008
710.77345 (not dirty, but spells "shell oil".) I like it because of how long it is. I wonder how long you can go with; 3=e,4=h, 7=L, 0=O, 1=I, 8=B, 5=S...
@@lolerskates876 57,738,461,375
Sleigh bells.
My favorite number is 8. Though it doesn't seem to have any special significance in Maths, there are two ways that it encompasses even the biggest mega numbers:
1. Turning the number on its side reveals the symbol for infinity, which as a concept would encompass every number in existence.
2. Thanks to digital clock patterns, we can see that 8 contains every single-digit number in the decimal list, which means that 888,888,888 would encompass your favorite meganumber pairing.
3. As a bonus, reversing #2 has been proven through magic tricks to be a useful way to mask a number's value. Simply draw the lines not pertaining to that number and it takes people a while to figure out what you wrote.
"Pattern fooled you" - Grant Sanderson
My favorite one is 30,041,777 (30/04/1777) because it’s prime and it’s Gauss’s birthdate
I was going to use DDMMYYYY or MMDDYYYY for any random birthday. Yours is better.
I love mathematical patterns that break. I feel it validates diversity. "It may *seem* like the obvious is always true... but it isn't."
Definitively out of my element here. Reading just a few comments. I look for a pattern that makes sense as learning is somewhat relational. Sometimes a pair of amicable numbers fail to rise from a multiple of nine. This anomaly presents itself as a fluke yet, its universally accepted letting one freaking number get away with abandonment? A true and good bridge lets patterns follow. Instead of, a disintegrating track midway. Still, miraculously, Locomotive #9 flies over virtual tracks of contradiction, camouflaging a pattern without form as invisible to imagination. A fare paid with discrimination isn't fair when acceptance incarcerates inner vision. How'd you get your favorite paired numbers? Something you had arrived at or willed to you by a smart person? Cool, thanks.
One of my favorite meganumbers is 3,816,547,290: The only number that is polydivisible and pandigital.
Here, sigma(n) = the sum of all divisors of the positive integer 'n'.
If sigma(a) = sigma(b) = a+b is true, then (a, b) is a pair of amicable numbers.
Conjecture: a+b is always a multiple of 9.
666,030,256 is the concatenation of a repdigit, a palindrome, and 2 raised to a power of 2
Hey James, you broke the rules and actually chose 2 numbers!!
Their sum is one number.
James: I'm gonna do what's called a pro gamer move
Pacvalham Yes, but he never actually said it in the video. Ergo two numbers.
@@OliviaSNava 4:10
TFW I didn't realize you had a channel and it's full of good stuff, been around for almost 15 years, longer than Numberphile itself, and the name is hilarious :-D
Ha! Welcome, I like to stay slightly under the radar.
@@singingbanana Thank you :-) I'm happy to be here! I suspect the #MegaFavNumbers project will bring more newcomers like me :-)
thanks for this challenge @singingbanana. Big fan of yours. Hope you add my MegaFavNumber video to the playlist, and keep making great videos.
That's wild! I love this story. The patchy conditions for failure are fun.
Thanks Tom! I've had that fact in my pocket for years and was waiting for the right video to drop it.
Excellent!
Thank You... thoroughly enjoyed 😊
Will post my mega no soon😎
Pretty cool numbers indeed.
Aha! I knew this couldn’t be a coincidence!
There should be a why is this number cool contest using numbers like this.
In middle school I memorized 7^8=5,764,801 for no reason whatsoever other than to brag about it.
Since then, I found out that 2^20=1,048,576, which is the maximum number of rows in Excel, has the same exact digits!
Thank you for calling it "Favo(u)rite Mega Number" and not "Mega Favo(u)rite Number"!
That makes a LOT more sense, it's been bothering me elsewhere.
I have a table to find a bit more easily the amicable numbers and not only, perhaps from that could derive a formula to find them.
I love these videos!!
wow! this guy looks exactly like the guy from numberphile!
I am working on a list of all the number over a million that are divisible by 2. So far, I have a lot of them. Research is continuing.
2:05 that transition really is something…
Browsing the OEIS for some good integers > 1,000,000 !
I'd call them "The a Joke of Developers of the Universe".
Of course its 666 M that stands out of the pattern
with the pair 696 (69, 96...)
Grimes you devil!
awesome idea
I wish you would upload more :) great Video
This is really cool info. Love those big numbers. I didn't know there was so much complexity and mystery when it came to these pairs. I'll see about making a video on my channel. :)
good to see you buddy
A number fails to resist the confrontation of an aggressive divider and dissolves into two equal smaller ones, and an attempt to gather every successful divider together and list them out is then being carried out. The transformation process from a number to a list of "more capable numbers" seems to end, but because of some unknown initiatives and with some unknown purposes, the dividers are being "merged in" to form one new number, eroding their independent state. The formed number seems to be able to compensate for the initial need of the person to withhold one number for a certain goal. The whole process can end right there, but by some reasons, the same "dissolving effort" is then being applied to the newly agglomerated number, perhaps wondering of how it would dissolve into and what the dissolved number list can agglomerate into again at the end. It is surprising to find out that the effort leads back to the original starting number, and what seems to be continuous ongoing processes of deminishing values and process progressing far away from the initial starting point actually brings the numbers back to the starting point. After the capability to return, the dividing purpose and effort can carry on to be made without fearing of deminishing of numbers or defying from the original starting position. And the return is done without additional help from efforts "out of the system".
Loved your video! I was, indeed, inspired to make my own, but I was on vacation and just made my video today, 4 days after your official deadline. Would be honored to be on the playlist all the same.
Done.
@@singingbanana Thanks -- for putting my video on the list and also for all your videos through the years. My first memory of a singingbanana video was on Simpson's paradox the day it came out. Keep up the excellent and inspiring work and stay well.
Wow! Thank you.
The sum of the 503rd pair isn't even divisible by three:
666,030,256 + 696,630,544 = 1,362,660,800 = 2^6 * 5^2 * 31 * 83 * 331 .
Why not use the Rule of 3 to prove it? 5+0+3=8 or 2*3+2
@@Maninawig
You mean the cross sum?
For completeness sake.
@@xCorvus7x I learned it as the Rule of 3: Add the numbers up and if it's a multiple of 3, then the number in question is divisible by three. As 5+0+3 does not equal a number divisible by 3, then the number cannot be a multiple of 3.
@@Maninawig Oh, okay.
Though, wouldn't the result for 1,362,660,800 be 2?
@@xCorvus7x 1+3+6+2+6+6+0+8+0+0=32 so 2 over 3*2. Sorry I thought you were calculating 503, though it's interesting that both equal to 3*2+2 when passed through the Rule of 3
2:06 now if you pause there, you got yourself a nice creepypasta
I like 1,000,001. It is the smallest possible integer MegaFavNumber.
My favourite number over a million is 2^24 = 16,777,216. The number of colours and shades a 24-bit graphics card can send to a display. Not all displays can actually display all of them (yes it's true,, even now some cheap displays can't manage it) but the card can output that many.
Will you make a follow-up video on Amicable numbers? I feel like they deserve more attention! 😊
The fabric of reality reveals itself through number theory. 503rd pair doesn't play ball.
Do the ratios have any interesting properties? Do they tend to a single value?
they tend to 1
@@joedoe3688 You got a proof for that, smart aleck? The difference between the pairs doesn't stay constant. It's possible it does tend to 1 but it would require more than 11 characters to write the proof.
@@nomukun1138 Chill out dude, it's not that serious.
@@caiheang I dont think he was being agressive. He just didnt choose the best combination of words. I also have the same question. Is there a proof that is understandable by us, youtube comments folks?
I can say with confidence that if there are only finitely many amicable numbers that the ratio converges to a single value. :p
I don't know UK's social security number sequence, but I do know that 3 groups of 3 numbers (starting with 6) is how Canada organizes their personal social security numbers.
Though I believe it could not be as the numbers are somewhat sequential, I think it would be super cute if your favorite number paring happened to be the social insurance numbers of an actual couple.
UK doesn't use Social Security numbers. We use National Insurance numbers. The format of the number is two prefix letters, six digits and one suffix letter. An example is AB123456C. Neither of the first two letters can be D, F, I, Q, U or V. The second letter also cannot be O. The prefixes BG, GB, NK, KN, TN, NT and ZZ are not allocated.
Yayy!
nice project!
my fav mega number is my secret key, and I won't be sharing that!
We need to come up with another math hashtag ASAP. This one turned out to be a success, bringing the global math enthusiasts community together. How cool is that?
1,000,001 is my favourite mega number. This is the smallest mega number which also has the additional property
.
"You should go watch all of those videos"
300 10-15 minute videos.
Please do another one of these playlists some time. I really wanted to make a video but couldn't finish it in time 😭
6,700,417 which is the large prime factor of F5 = 2^(2^5). Lower numbers 2^(2^n) are all prime, but Euler (again!) showed that F5 is 641 x 6,700,417
you forgot a +1 after the = sign
@@GamerDuDimanche1456 Gah, of course, 2^(2^n) + 1, silly me.
What is up cool and rad math lovers ? You must come watch my new #megafavnumbers video. It is the greatest number video out and It will enlighten you! -CodyTheKingOfRUclips
i
Love your videos, something I noticed in about 4 of your most recent videos is that your exposure settings for your camera are always set incorrectly. Take care!
The linked paper starts:
"An amicable number pair is a pair of numbers, M, N, satisfying σ(M) = M + N = σ(N)"
That definition seems completely different from the one in Wikipedia (which is the same as what James said in the video).
I think that's equivalent. sigma is all the divisors, not just the proper ones.
σ(N) is the sum of all divisors, including N.
Let s(N) be the sum of proper divisors of N.
σ(N) = s(N) + N.
So σ(N) = M + N is the same as s(N) = M.
Both definitions are equivalent.
Mine is 2 ^ Graham's number, because it is even
nice
Happy Pi Day, James!
Thanks for this project. It makes me discover toutube mathematicians I didn't know. But I don't see Professor Penn there ;(
Sounds like what you said for skewes number.
I don't know a lot of neat math(s) stuff like you do. So, i'll just say my favorite mega number is 1,000,000 + 1,000,000 i.
So perfect numbers are self-amicable.
Are there relationships between amicable numbers and perfect numbers?
I'm not sure what my favorite meganumber is, but 52631578947368421 is up there, since it's the smallest number which when doubled, has all its digits shifted one place to the right.
Deceptive patterns like this are the Collatz conjecture is still considered unsolved. A conjecture.
Hi. My favorite mega number is 1000001. That is smallest integer that fits the "definition" os mega number (bigger than one milion).
5,318,008. I'm so immature😂
Dont get it bro...
@@cosimobaldi03 If you write it in a seven segments display (like a calculator), and read it upside down, it resembles the word "BOOBIES"
If you care about 3215 the larger ones are 5318008918
Euler doing Euler things
Which one of the pair is your favorite?
epic
Euler 💪🏼💪🏼
You just remind me of Bricktop in Snatch but you are far more pleasant.
Question: Could this question of finding amicable numbers be a solution to P = NP (similar to that of the traveling salesmen)?
It's relatively easy to check whether a set of numbers is amicable numbers, but it could be challenging to find new amicable numbers, of course then you'd have to ask whether it's then easy to check if you have *all* of the amicable numbers, but say your goal was just to find a new one would that even work to satisfy P = NP even if it was true?
my fav nr is 1Mil. its what i want every month
No fair, this guy got two numbers
if you pause during the white flash transition at 2:06 you can get some creepy faces lol
My Fav Mega Number: 1,000,001 (smallest Mega Number)
Bringing back RUclips video replies, how exciting.
I always liked RUclips replies, and miss that aspect.
I don't pick favorites. I love all numbers.
2^32 because stroustrup
is there such thing as an amicable trio?
like x -> y
y -> z
z -> x
if so, that'd be a very cool video concept!
Sociable numbers: en.wikipedia.org/wiki/Sociable_number
Apparently there aren't any known trios but there are known sequences of 4, 5, 6 and more numbers.
Joan Charmant that's awesome, thank you so much for sharing this :)