@@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.
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!
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
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
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
@@paintspot If I had a nickel for every time I accidentally thought a woman was a dude, I'd have two nickels, which isn't a lot but it's weird it happened twice.
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
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!
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.
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
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'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.
13:21 Who else noticed that the proper divisors of n looked almost like the nth binary term? I'm sure this is no coincidence, but I'm not smart enough to find out why this is. Also, I love the vids Kuvina!
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 :)
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
70's factors: 1,2,5,7,10,14,35,70 Sum of proper divisors: 74 Closest 70 can get: 69 (74-5) I've actually came up with a new weird number called "Near Weird Numbers." They are a Near Perfect Number but isn't Primitive Abundant nor a multiple of a Perfect Number and the only one below 1,000,000 is 40
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.'
1:58 What a coincidence. A few weeks ago, I thought of a metric to quantify exactly this. I referred to it as imeness. Every multiplication by a prime number increases the imeness by 1, and every division by a prime number decreases the imeness by 1. That was how I extended the notion of imeness to any rational quantity on the positive side of the number line. Then I made the adjectival forms by using pseudo-Greek prefixes followed by -prime, using biprime instead of semiprime. I can now confidently say that one is a nullaprime, and zero is a negapeiroprime.
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.
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
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.
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
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"
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)
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.
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).
There's another type of "high abundance" that probably has another established name already but I like to call "highly heterogeneous" numbers, the smallest number with the most UNIQUE prime factors. The method for generating them makes them maybe too easy to be interesting; they are 2, 2x3=6, 2x3x5=30, 2x3x5x7=210, etc., but I was looking at numbers in different systems and I found the highly heterogeneous numbers themselves very interesting. The pattern for generating them is still the same, simply take the prime with the lowest magnitude that isn't yet a factor, and throw it into the list of factors. In Eisenstein numbers this is 2+ω, 4+2ω, 10+2ω, 28+14ω, 98+28ω, . . . (and each of them have 5 or 11 associates). I don't know why but they just feel more interesting to me.
oh I just looked them up in the OEIS, not sure why I didn't bother to do that earlier, they're called the "primorial" numbers which is probably a better name than what I came up with
@@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).
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
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.
This video now has a sequel, the Almost perfect numbers! th-cam.com/video/qQk0lzSDpZs/w-d-xo.html
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.
8:29 im noticing an "add 12 to this number to get the next number" pattern here
Except that obviously wont work with 1 and 6
hey Kuvina, I noticed you listed 28 twice at 0:20 or so
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?
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
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
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
6
Mathematicians: Beautiful. Elegant. Perfect.
7
Mathematicians: Disgusting. Horrid. Unusable.
what about 528
9
Mathematicians:
7: eaten
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
These math vids are insane, as a nerd I ask you to continue making these.
Weird? They're not even odd!
hahahahahhahahahahahhahahahahahah😊
Good one!
Nope, not as far as we know!
That’s, exactly, what makes them so weird. I’m also acutely aware of the possibility of logical loops, here. They only add to the weirdness.
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.
@@btf_flotsam478this guy explains better than Wikipedia, reading for information is over
My little sister heard this and kept making sigma sigma boy jokes
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.
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.
Kuvina’s not a dude.
-Paintspot Infez
Wasabi!
@@paintspot If I had a nickel for every time I accidentally thought a woman was a dude, I'd have two nickels, which isn't a lot but it's weird it happened twice.
I’m tempted to make up a base-70 numeral system and make people suffer using it
I love how naturally your story moves towards these practical numbers.
Please continue making videos like this. Your views may be low but be sure your videos are very valuable and we know that.
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
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!
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.
0:35 quest for perfection instantly brought me old gd times back
GD MENTIONED RAAH
GEOMETRY DASH
GEOMETRY DASH dun dun dun dun dun da da da da da da da da
geometry dash
@@kristinborn8882 Three... Two... One... GEOMETRY DASH
Really enjoyed this! The progression of concepts was paced nicely imo.
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
This is one of the most intuitively well explained math videos I’ve seen
I mean for me its just simply
Even:not prime
Odd:idk cant bother to check
Odd:Sometimes prime
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.
OMG THE PIN ON UR SHIRT IS SO CUTE
Your voice is so relaxing, makes me feel calm and safe.
You should make compilation of your videos to fall asleep to
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'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.
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!
13:21 Who else noticed that the proper divisors of n looked almost like the nth binary term? I'm sure this is no coincidence, but I'm not smart enough to find out why this is. Also, I love the vids Kuvina!
I might use this as a reference if I make a number 70 Algebralian OC...
Amazing video as always! Thanks for sharing this sequence of numbers
6:36 Veritasium made a vid abt this excact concept.
Very interesting vid.
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
I love your videos
these have great quality
For some reason this has become my comfort video, I’m watching this for the fourth time now
i was just reseraching this topic as tangent of highly composite number huh
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! 👍
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
I enjoy the notion of viewing the characteristics of a number as that number's "personality". It's fun.
70's factors: 1,2,5,7,10,14,35,70
Sum of proper divisors: 74
Closest 70 can get: 69 (74-5)
I've actually came up with a new weird number called "Near Weird Numbers." They are a Near Perfect Number but isn't Primitive Abundant nor a multiple of a Perfect Number and the only one below 1,000,000 is 40
All I have to do is find a very large prime number and MULTIPLY.
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.'
1:58 What a coincidence. A few weeks ago, I thought of a metric to quantify exactly this. I referred to it as imeness.
Every multiplication by a prime number increases the imeness by 1, and every division by a prime number decreases the imeness by 1. That was how I extended the notion of imeness to any rational quantity on the positive side of the number line.
Then I made the adjectival forms by using pseudo-Greek prefixes followed by -prime, using biprime instead of semiprime. I can now confidently say that one is a nullaprime, and zero is a negapeiroprime.
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.
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
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.
Don’t forget literally any number with a factor of 17
This is as beautiful as it is useful, thank you for making this.
Beautiful video. I shall never see 70 the same way
not as many views nor comments as I was expecting, hope yt boosts this more
i have no idea what happened but i loved it
Always wanted to praise some numbers
I found a video next to it that had a stopwatch on 8h 36m
I love your channel!!
70 is weird because I usually fail to divide it by 2 when doing quick math.
This is why i hate maths questions with values like 70, they are not hard, but 70 IS STILL TO BE HATED.
This makes me wonder if you know about veritasiums 37 video. both of these are EXCELLENT videos, although i do like urs more :3
i wanna be a perfect number when i grow up
wait til your 28th birthday then
i am happy to say that at the start of the vid i guessed the weirdest 3-digit number as 834
The Smallest Weird Number - Geogaddi - Boards of Canada. This song is literally ends on 70 seconds.
Any number involving seven is an abomination
Except for 37 and 137, even though latter is a bit unhinged
does this mean if a test is worth 1000 points, I have to score a 836 or above to pass?
I almost had a heart attack when I thought 836 before you said it
I knew it would happen eventually 😎😎
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
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"
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"
100000001 can be divided by 17
This scares me
Awesome video :)
your little avatar's squiggly arms are so silly, i love it :D
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)
omg i swear you have all the same interests as me!!
i love watching your videos so much, thanks for making them! :3
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)
ive been watching you for a year or so, so its about time i comment and sub lol
I dont know why but I watch these kind of videos not even knowing the math
Poor 70, his brother 88 always calls him weird. What a bad personality.
Which number has more factors?
96 or 100?
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.
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).
11:46 720720 popped up somewhere else I forget where. I was studying certain divisibility series.
There's another type of "high abundance" that probably has another established name already but I like to call "highly heterogeneous" numbers, the smallest number with the most UNIQUE prime factors. The method for generating them makes them maybe too easy to be interesting; they are 2, 2x3=6, 2x3x5=30, 2x3x5x7=210, etc., but I was looking at numbers in different systems and I found the highly heterogeneous numbers themselves very interesting. The pattern for generating them is still the same, simply take the prime with the lowest magnitude that isn't yet a factor, and throw it into the list of factors. In Eisenstein numbers this is 2+ω, 4+2ω, 10+2ω, 28+14ω, 98+28ω, . . . (and each of them have 5 or 11 associates). I don't know why but they just feel more interesting to me.
in Gaussian integers the sequence would be 1+i, 3+i, 5+5i, 15+15i, 15+75i, . . .
oh I just looked them up in the OEIS, not sure why I didn't bother to do that earlier, they're called the "primorial" numbers which is probably a better name than what I came up with
What if there was a sequel called “71 is odd”?
13:42 Shouldn't it be 11² in the last one?
Also, how is sigma(1) = 2?
I don't like how much of this I know from random wikipedia rabbit holes
70 and I have a lot in common.
Base 70 is a perfect system with no flaws whatsoever.
I dont even want to know what that would be
i like your funny words, magic man
Ah, number theory, a subset of mathematics I'm not too excessively interested in
I'm 70, I'm weird.
i dont know and care about what your talking about but i think you're right..
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).
this video gives me the same feelings the jan misali math videos do
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.
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
Cool video!
This is aweseome
i've been hearing waltz of the flowers everywhere im going crazy
Great video as always, not much of a number theory person myself, but I still had a lot of fun
Oh my Euler, I guess I found some good channel.
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.
03:46 I don't understand this table, it doesn't look consistent. For example, haven't 6 and 10 each got 3 divisors?