70 is weird
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- Опубликовано: 7 апр 2024
- In math and number theory there are many sequences of numbers and one of the most interesting ones is the weird numbers! In this video, we examine the motivation behind them, especially abundant numbers, deficient numbers, perfect numbers, highly composite numbers, and practical numbers.
#math #70 #numbers 
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I hope you enjoyed the video! Also happy eclipsing! 🌞🌑
back with another banger as always & carrying whatever's left of good on this internet 💥💥💥💥💥🔥🔥🔥🔥🔥🗣🗣🗣🗣🗣🗣🗣♥♥♥♥♥
I really enjoyed it! Sadly, I don't live in America, so i didn't see the eclipse.
@@tntdude999besides the eclipse, you should be glad you dont.
Its interesting how we subconciously see numbers as "more or less prime" despite not knowing mathematically why
what do you mean? we know why
@@mrosskne Yes, but one who doesn’t know mathematically why the interesting thing is that they still see numbers as more or less prime.
@@mrosskne mathematicians or people with knowledge about number theory can articulate how some numbers are more "composite" than others.
but people with no mathematical knowledge can still have a vague intuition that, for example, 22 is more "prime" than 20, but they won't know why they feel that way
@@wpbn5613I think it's because we are taught that anything with a 0 at the end is divisible by 10. This makes a number feel "full". 0 is also shaped like a circle and is symmetric. 2, 4, 6, and 8 don't feel like primes because we can split them in half, 5 because it's half of 10, 3 because it's seen everywhere, 9 because it can be split to 3. 7 feels odd because it's not 2 or 4 or 6 or 8, it's also not seen as common as any other number, and it's weird when counted. It's not between 0 and 10, it's between 5 and 10. It's also the only single digit number (excluding 0) that has two syllables.
@@MrBrineplays_ i feel like your reply isn't very related to what i said?
Weird? They're not even odd!
hahahahahhahahahahahhahahahahahah😊
Good one!
Nope, not as far as we know!
12:52 the french pronouncing numbers
As a french, I validate the joke.
@@Zorg06Scratchok
20 times 5 plus 9 times 3
yeah but then 90 is wierder than 70
10 dozen + 1.5 adults = 147
70 here, and I would like to verify this: I am in fact a bit weird.
as 836, I am also weird
@@kristinborn8882 4030 here, same
hey guys, 5830 here, I can also confirm I am a bit weird too
you younglings dont know how it feels to be 7192
@@alesonbrjk 7912 walks in
Pausing halfway through the video to say this is the first time I've ever seen an explanation of perfect numbers that feels compelling at all. I never understood in what context their usual definition was supposed to matter at all, and this helps it make a lot more sense!
Thank you! It was tricky, but my goal for this video was to tie the concepts together in an order that actually makes sense.
I literally pressed pause on the video and said out loud "OHHHH" when I heard "and those are called perfect numbers" because I finally understood wtf it meant
your feelings are irrational
And here i thought 37 was random
37 has always been my go-to lucky, random, whatever number for a million different things. And all of a sudden, in the past month or so, I've been seeing it everywhere
Probably because of the Veritasium video
Not even, its just a weird looking and ugly number. Its prime, its digits are prime, it has a prime amount of digits, and it ends in 7 and 7 is weird and lucky @razdahooman
@@razdahoomanSame, i use 17, 37, and 87
37% is close to 1/e
I should be doing something but instead I'm watching some dude on the internet insult the number 70 in the most overly complicated way imaginable.
yeah, i have no clue whats going on
Wikipedia exists, stare at all the factor-based stuff for a bit and it kinda makes sense.
And I thought 70 was weird because it was just 60 + 10.
damn you, french!
Wait till you hear about 80
@@lePirateMan I don't see any issue with huitante. /s
Quatre vingt dix is worse
90 is worse. (4*20) + 10.
the weirdest number for me is 193
but thats only because every single time i bought lunch in college my number to pick up the food at the restaurant it rung up 193
These math vids are insane, as a nerd I ask you to continue making these.
6
Mathematicians: Beautiful. Elegant. Perfect.
7
Mathematicians: Disgusting. Horrid. Unusable.
Please continue making videos like this. Your views may be low but be sure your videos are very valuable and we know that.
as an autistic person with a special interest in math i especially like the idea of thinking of numbers as having personalities, so this is a great video for that!! 70 is a Weird Little Child and i love them for it :)
acoustic
Very interesting video! Here are a few of my favorite interesting facts about sums of divisors:
1. Euler found a pretty amazing recursion for σ(n):
σ(n)=σ(n-1)+σ(n-2)-σ(n-5)-σ(n-7)+σ(n-12)+σ(n-15)-σ(n-22)-σ(n-26)+...,
where the signs are +,+,-,-,+,+,-,-, etc. the numbers 1,2,5,7,... are pentagonal numbers, and we count σ(0) as n if n is a pentagonal number. This comes from his pentagonal number theorem, and a very similar recursion is also valid for the partition function p(n) (the only difference being that p(0) is counted as 1, not n as in the case of σ).
2. The Riemann hypothesis is equivalent to σ(n)5040, where γ is the Euler-Mascheroni constant.
3. A number satisfying σ(n)=2n+1 is called "quasiperfect", but none are known to exist. It's known that if any do exist, they must be odd squares larger than 10^35.
Loved this! Got to learn about several new categories/sequences of numbers and your graphics convey so much meaning and understanding. Thanks for making my Monday, hope yours was great and I'm looking forward to the next video as always!
Really enjoyed this! The progression of concepts was paced nicely imo.
By the end you had defined so many new terms that it was impossible to keep them all in my head. Really interesting video though
All of this stuff is on Wikipedia (if you want to revise).
I love this! I've watched a lot of math videos and read many pop math books in my day. Many of them talk about perfect numbers (to the point of nausea) and this felt like a fresh take on the subject.
I’m tempted to make up a base-70 numeral system and make people suffer using it
I've investigated the sum and count of factors and have made tunes based on them, adding them into oeis too. This is a neat and fair way to go about it! However I like excluding 1 from these sums and products because it's in everything.
Amazing video as always! Thanks for sharing this sequence of numbers
This is one of the most intuitively well explained math videos I’ve seen
0:35 quest for perfection instantly brought me old gd times back
GD MENTIONED RAAH
GD reference 🤓
GEOMETRY DASH
GEOMETRY DASH dun dun dun dun dun da da da da da da da da
geometry dash
i was just reseraching this topic as tangent of highly composite number huh
I might use this as a reference if I make a number 70 Algebralian OC...
Me tracking 70 throughout the video trying to guess why 70 is weird before they say it
Just so u know, they use they/them pronouns :)
@@RKade01 thx!
This was a great video man well done
I LOVE THIS WAY OF LOOKING AT NUMBERS! It feels like innate truths are being revealed in a way that flimsy addition or subtraction could never manage. And getting to have personlaities, vibes, feelings and characterisations applied to numbers in a rigorous way is anazing
your feelings are irrational
Any number involving seven is an abomination
This is as beautiful as it is useful, thank you for making this.
I mean for me its just simply
Even:not prime
Odd:idk cant bother to check
Odd:Sometimes prime
I love your channel!!
i wanna be a perfect number when i grow up
wait til your 28th birthday then
This explains why I've always liked 2, 5, and 7. I "hate" 3, and 11 is bigger than 10, so i have a more neutral opinion about it.
I used to explain it as.
1² + 1 = 2
2² + 1 = 5
2 + 5 = 7
3² + 1 = 10 = 2 × 5 (i like base 10 more than bases
divisible by 3)
7² + 1 = 50 = 2 × 5 × 5 = 5² + 5²
Loved the video bro. subbed
If you like the Egyptians having five spare days to finish off the year, then I think you'll like that a similar tradition exists in Mesoamerican year counting, in which there was an extra week of days which had no deity or spirit watching over, so which led to that week being thought of as a sort of 'chaos week.'
ive been watching you for a year or so, so its about time i comment and sub lol
i love math videos bc 80% of the time they make my head spin but 20% of the time i understand something or notice a pretty pattern and i'm like "woahh that's pretty cool" it's like gambling for my pattern seeking neurodivergent mind
I almost had a heart attack when I thought 836 before you said it
I knew it would happen eventually 😎😎
not as many views nor comments as I was expecting, hope yt boosts this more
does this mean if a test is worth 1000 points, I have to score a 836 or above to pass?
Awesome video :)
Wow! That was a ride! Thanks for the video! I'd better go now and make sure my aliquot is abundant, or, at least semiperfect, before I continue! 👍
omg i swear you have all the same interests as me!!
i love watching your videos so much, thanks for making them! :3
i am happy to say that at the start of the vid i guessed the weirdest 3-digit number as 834
All I have to do is find a very large prime number and MULTIPLY.
As a Pokemon player, this is 70% accurate
I found a video next to it that had a stopwatch on 8h 36m
70 and I have a lot in common.
70 - divisible by 7
836 - its a weird multiple of 4
4030 - between 4000 and 4096 and divisible by 10
5830 - once again ends in 30, near 5776 = 76²
7192 - 1000 off of 8192
For me 544 looks like a number that's probably only divisible by 4, but it's actually divisible by 32.
Personally im the #1 hater of primes of the form 4k+3 (and numbers divisible by them) since they can't be written as the sum of squares.
its an open question whether there are any odd weird numbers
More interestingly, it is an open question if there are infinitely many primitive weird numbers.
Multiplying a weird number by a prime number larger than the sum of its divisors (including the weird number itself) also gets a weird number, but these are not considered primitive weird numbers.
8:11 Here, I immediately wondered what the primitive abundant numbers with the highest abundance are (or if it increases) and if there are an infinite number of them (also: glider in top left at 14:06)
I'm 70, I'm weird.
1: Foundation of numbers
2: The first and only even prime
3: The second prime and the perfect number
4: Is considered unlucky in Cantonese culture
5: Five fingers
6: A dice has 6 faces
7: Considered lucky in pop culture
8: Is the second cube
9: It's a square
10: A decade is 10 years
11: There are 11 players in a football team
12: There are 12 sides in a dodecahedron
13: It's considered unlucky in pop culture
14: It's the maximum age for puberty for teen [boys]
15: It is a result of summation from 1 to 5
16: It can be written as 2^2^2
17: This can be considered as an age for entering adults
18: It has an inverted factor [12 is 2×2×3 while 18 is 2×3×3]
19: It's the first non circular prime
20: There are 10 fingers and 10 toes, which, sums up to 20
21: It's a perfect number times the lucky number
22: There are at most 22 players in the football field
23: Is the maximum number in a digital clock as thr next hour will be 0
24: There are 24 hours
25: It is the last odd number that can divide 100
26: A rubix cube has 26 parts [not including the core]
27: A rubix cube has 27 parts [including the core]
28: It is the second perfect number and is a summation from 1 to 7
29: There are 29 days in a leap year in february
30: There are 5 months that have 30 days
31: There are 6 months that have 31 days
32: There are 32 white tiles and 32 black tiles in a chessboard
33: It is 100001
34: R34 [So sorry]
35: Is 50 in base 7
36: Is made from 2 different square
37: Is one of the least random number [credit to veritasium]
38: It is 212 in base 4 [which is palindromic]
39: If it's base 16, it's 27
40: From base 9 to base 2, it's 100100
41: It is the 3rd number that can be made into a rhombus by block
42: To Base 2 is 101010
43: Is the first NON chen prime
44: A semi-final consist of 4 teams, each having 11 players
45: it is a summation from 1 to 9
46: Is an Erdős-Woods Number
47: Is a love number
48: It is a highly factorizable number after 24
49: Is the first number that cannot be checked easily whether if it's a prime or not from 1-100, as it's not even, doesn't end up to a divisor of three by summing the digits, doesn't ends with a 5, and is not repeating.
50: Is the center from 0 to 100
You wrote 33 twice
Oh. Thanks
42 is the answer to life the universe and everything
What if there was a sequel called “71 is odd”?
Reminda me of the song "The Smallest Weird Number" which is... well... 70
funny cause boards of canada own a label called music70, and the melody in the track ends at 1:10 (70 seconds)
the way mathematicians talk about numbers is so cute
The thumbnail is so out of context for people who don't know about that kind of mathematics
I just thought we were talking about how some numbers aren't very used for specific reasons, and also numbers personalities
but o will say, I was not expecting 50 to be called "deficient"
Always wanted to praise some numbers
Ah, number theory, a subset of mathematics I'm not too excessively interested in
In my opinion, the weirdest numbers are ones with a 3, 6,7, or 9.
Those numbers just look so damn bad that everytime I make something with having to write numbers in it, I somehow find a way to make every number look "perfect"
Base 70 is a perfect system with no flaws whatsoever.
Cool video!
your little avatar's squiggly arms are so silly, i love it :D
1:40 34/2=17
Also 61 is less prime than 67 and 63 is the oddest number under 100, and 65 is the most even odd number under 100
100000001 can be divided by 17
i have no idea what happened but i loved it
6:36 Veritasium made a vid abt this excact concept.
Very interesting vid.
Beautiful video. I shall never see 70 the same way
70 is weird because I usually fail to divide it by 2 when doing quick math.
Great video as always, not much of a number theory person myself, but I still had a lot of fun
OMG THE PIN ON UR SHIRT IS SO CUTE
I don't like how much of this I know from random wikipedia rabbit holes
your voice sounds like i've heard it for years but i've never watched one of your videos
i like your funny words, magic man
this is my favorite math video in a long time!!!!! i love number theory and i've learned a lot of interesting recreational facts, but this was delightfully new to me and even more delightfully presented by you. thank you so much, this was lovely to watch and learn about. you are amazing! i subscribed and can't wait for more of your content
14:25
Legendre is definetly true. As the distence beteen 2 neighboring perfect squares gets increaingly big. Granted its only by 2 more each pair, but it does add up over time.
Twin is probably true, given how primes can only exist agencent to multiples of 6. And all 4 possibilites (both are prime, +1 is prime, -1 is prime, and neither are prime) would probably happen infinietly with infiniet numbers, there should be infinite twin primes.
Im not sure about Goldbach's though. As we would need to check every even number to see if any even numbers bigger than 2 arent the possible sum of 2 primes.
The average difference between primes also grows, and there's infinitely many pairs of square numbers that could have no primes between them.
By the way, very similar evidence exists for either of them being true, and it is widely believed they both are.
Which number has more factors?
96 or 100?
11:46 720720 popped up somewhere else I forget where. I was studying certain divisibility series.
why does it say primes are higher than composites? they're at the bottom of the graph.
Man, some people have too much time on their hands to think of this stuff. It's interesting for sure, but like, I don't even have the free time to do my laundry regularly, and there are people out here organizing numbers into superficial categories.
Oh my Euler, I guess I found some good channel.
At 6:00, why are there so many numbers whose aliquot sum is equal or almost equal to n/2?
Those are prime numbers times 2. Their only proper divisors are 1, 2, and n/2.
Old money was far better than decimal. 12 pence in a shilling and 20 shillings in a pound made 240, ha'pennies gave us 480 and farthings gave us 960: all practical numbers. 240 is also highly composite.
i did learn something, thankyou kuvina!
I'm so confused
What does the prime factors being "in order". Can't you just arrange them in ascending order? I thought maybe it had to do with increasing powers... But your example
They explained it immediately after: Every prime factor is less than or equal to the sigma of the factors smaller than it.
(ie, the prime factors are close enough together).
I think 19 is weird cuz
1.its my birthday
2.It has a very VERY interesting name in french
DEEZ NU-
this video gives me the same feelings the jan misali math videos do
The Smallest Weird Number - Geogaddi - Boards of Canada. This song is literally ends on 70 seconds.
Not a bad thing but you have a math accent
Oh shit here we go again
This is so simple, I understood it all at once!
Those who spend years studying this by getting PhDs and stuff must be slow or something.
[/Irony]
It's dense with information but at the same time also a great introduction to the topic, that's what I love about this channel
@@hydrocharis1 I love it too! The superiority of online lectures is that one can pause and look stuff up. And hear it again. That was difficult to do in the traditional physical lecture hall.
Also, the online lecturer can plan and produce in a much better way than what any physical real-time university lecturer could. Perhaps having a bad day when repeating the same bloody live performance for the 100th time. Wanting to do maths instead of acting on the scene infront of a bunch of stupid 20 years old.
@@bjorntorlarsson It also doesn't hurt that this topic is easier to understand than the ones taught in standard mathematics courses; there's a reason number theory was explored so thoroughly before stuff like calculus was invented (and also that it gets more interest recreationally).
03:46 I don't understand this table, it doesn't look consistent. For example, haven't 6 and 10 each got 3 divisors?
70 is also 1 after 69, which is weirdly nice.
Me before watching this video thinking I was good with numbers: 😎
Me giving up after seeing there are still another 5 minutes of explanation for why 70 is weird:😐
This video is great, I wish I could say something worthwhile in this comment section
Wow!