Part 1 of this three-part interview is at: kzread.info/dash/bejne/nJyDxK6NYa_YltI.html Part 3 of this three-part interview: STILL BEING EDITED

@FebruaryHas30Days

Жыл бұрын

First reply

@Anonymous-df8it

Жыл бұрын

Second reply

@volodyadykun6490

Жыл бұрын

Still

@Anonymous-df8it

Жыл бұрын

@@volodyadykun6490 Fourth reply

@Jono4174

Жыл бұрын

Skewes’s number-th reply

Suddenly out of nowhere, a Function named after Euler appears. Feel like that's a fundamental rule of mathematics

@zmaj12321

Жыл бұрын

Euler's totient function is REALLY essential to anything involving number theory. Not surprising.

@tyle.s9084

Жыл бұрын

@Paolo Verri And Gauss always found out about it when he was four years old

@otonanoC

Жыл бұрын

Everything in math was invented by Euler or Riemann.

@louisrobitaille5810

Жыл бұрын

@@otonanoC Euler or Gauss* 😝. Riemann just built a few things on Gauss' work 👀.

@tommihommi1

Жыл бұрын

@@zmaj12321 I only knew it as doing some neat thing for RSA.

"Prime numbers are, like, the sexiest numbers available" Grant Sanderson, 2022

@1224chrisng

Жыл бұрын

as James Grime would point out, we do have Sexy Primes, twin primes with a gap of 6

@birdbeakbeardneck3617

Жыл бұрын

Shheeeeeshh

@lonestarr1490

Жыл бұрын

@@1224chrisng Dude! There might be children reading this thread!

@dyld921

Жыл бұрын

Grant Sanderson is, like, the sexiest mathematician available.

@kadefringe

Жыл бұрын

I phap on prime numbers indeed

An unlisted video from an unlisted video? Now we're in a super exclusive club!

@krokorok_

Жыл бұрын

:D

@viliml2763

Жыл бұрын

What video did you come from? I came from a listed video.

@mxlexrd

Жыл бұрын

@@viliml2763 It wasn't listed when I made the comment

@ophello

Жыл бұрын

The first video wasn’t unlisted.

@themathhatter5290

Жыл бұрын

@@ophello It was when Grant linked it in his own video

That silently-corrected "1/3" at 3:38 may be the first error I've ever seen Grant make 😂. The man is as smooth as an infinitely-differentiable function.

@theadamabrams

Жыл бұрын

For anyone confused, the correction 1/3 → 2/3 happens around 3:49

@berryzhang7263

Жыл бұрын

Omg yeah I was so confused when I saw the error lol

@leftaroundabout

Жыл бұрын

If he didn't make any errors _at all_ he would be smooth like an analytic function. But that would be boring, because then you could represent him entirely by his Taylor expansion. _Countably_ many values, that can't be enough!

@axp_bubbles

Жыл бұрын

If you watch the live streams he did during early pandemic days he makes a lot of errors while writing, and is very candid about them. Just a genuinely humble and brilliant human being.

@SmileyMPV

Жыл бұрын

@@leftaroundabout not all smooth functions are analytic though but any continuous function is still determined by its rational evaluations, so in order to not be determined by only countably many values you do need to be discontinuous :P

The length of successive Farey sequences is OEIS A005728. The Euler totient function is one of the foundational objects of number theory. The fact that the sequence here is one plus the sum of the first n values of the totient function is another of those neat links that almost feel numerological in nature. If memory serves, there have already been Numberphile videos on the link between the Stern-Brocot tree and Farey sequences on the one hand, and Farey sequences and Ford circles on the other.

Its a special talent to make your thumbnails consistently look like something out of the 90s

Grant's explanation is awesome, but Brady's analogies make it more accessible to everyone.

Is the third video ever coming? Have been checking back since this one first dropped

Grant: "1/5, 2/5 --" me: "red fifth, blue fifth"

@ps.2

2 ай бұрын

Oh, what a lot of fifths there are!

Amazing connection between Euler totient function, Farey and mobius inversion in such a short video.

We're reaching levels of unlisted that shouldn't even be possible

@viliml2763

Жыл бұрын

What video did you come from? I came from a listed video.

@Vaaaaadim

Жыл бұрын

@@viliml2763 part 1 When 3B1B's vid came out today, it linked to part 1, which was unlisted at that time.

Your original video on farey sums and ford circle packing is probably my favorite on this channel, and one of my favorite on all of the internet. To watch them suddenly come up in this video was truly a treat

@jazermano

Жыл бұрын

Since I read your comment and got intrigued, I went and found the video, titled "Funny Fractions and Ford Circles." It's dated at being roughly 7 years old. But it is still has the same awesome Numberphile feel to it. Nice to see some things haven't changed.

@redtaileddolphin1875

Жыл бұрын

@@jazermano aw thanks! it’s honestly asmr for me I love how he says “probably” and “pinkie”. 10/10 all math videos should also be asmr

It's like if you watch only 3b1b videos you would think everyone is as attractive as Grant

The sum of digits of that last sequence is not 33, it is 37, which is prime :) (if you count 10 as two digits).

@scottabroughton

Жыл бұрын

But if you insert 10 11s, it comes to 57, which is composite.

@gaborszucs2788

Жыл бұрын

​@@scottabroughton except that for example it's not 1+10, rather, 1+1, which is not 11, so you skip that, plus 10+1 at the end. 57-2x2 is 53 which happens to be a prime... Who'll volunteer for 12?

@scottabroughton

Жыл бұрын

@@gaborszucs2788 Can you provide a visual?

3 3 Blue 1 Brown Videos in 1 Day😁 Inception much?

7:14 So, we can define it as a function based on the Euler's totient function. one of the definitions of ETF is: phi(n) = sum from k=1 to n of gcd(k,n)*cos(2pi*k/n) then, the sequence would be defined as: 1 + phi(1) + phi(2) + phi(3).... or to rewrite: g(t) = ([sum from n = 1 to t of phi(n)] + 1) and, it still outputs primes even after the break omitted values denoted with ( ), erroneous with [ ] g(t): 2, 3, 5, 7, 11, 13, (17), 19, 23, 29, (31), [33], (37), (41), 43, 47, (53), 59, (61), [65], (67), (71), 73, (79), [81], (83), (89), 97, (101), 103 i mean yes, it breaks worse each time but the only erroneous values up to 100 are [33], [65] and [81]

@lonestarr1490

Жыл бұрын

So all we need is a different imperfect prime sequence to use in conjunction with it, where it is guaranteed that the two of them never fail at the same time.

@panadrame3928

Жыл бұрын

The question then is what is the proportion of non prime sums of φ(n) for n

@Michael-cg7yz

Жыл бұрын

@@panadrame3928 you mean this g(x) or Euler's totient function? I'm fairly sure the first one is independent of primes, so sometimes it'll hit them, sometimes, and that being the larger amount it'll miss them

probably the most fascinating prime pattern that tricks everybody the most is the approximating prime-counting function which leads to the birth of skewes number. even tho skewes number is an over-overestimate i guess the actually point where the prime-counting function changes its size comparison to the actual number of primes < n would still be something huge (like 10 to the power several hundreds?). this completely blasts through the regime of small numbers a mortal could interpret of, but yet at some point the relatively big boys still gonna break the pattern.

Funny how Grant can talk about a sequence of numbers that really doesn't have any sort of significance, and I still enjoy watching it.

Grant is always such a delight

I hope part 3 won't be unlisted. If I don't get notified when it's uploaded, I'll probably never see it.

I check back every day for Part 3.

@neil5280

Жыл бұрын

Monday was pretty chill.

@neil5280

Жыл бұрын

I don't have the stamina for commenting any more, but I am checking daily. Look forward to Part 3 whenever it arrives.

@neil5280

Жыл бұрын

Happy New Year! 🎉

I have been coming back here like twice a day waiting for part 3 to be linked in the pinned comment or description! I'm excited for that vid, I could listen to Grant talk about math forever

@deadlyshizzno

Жыл бұрын

I'm still checking!

@deadlyshizzno

Жыл бұрын

Why is it still being edited 😭

@deadlyshizzno

Жыл бұрын

D:

@deadlyshizzno

Жыл бұрын

I suppose the third video in this series is somewhere in the backlog now

@deadlyshizzno

Жыл бұрын

:(

Great mathematician. Great KZread content creator. Charismatic as heck. We all wish to be Grant I presume.

Is part 3 still in the works?

@joelkronqvist6089

Жыл бұрын

Seems like it was published today

After realizing that the total number of DIGITS in the 10th row stays prime (37), I got hopeful that maybe the number of digits would keep the pattern even if the number of elements (numbers) doesn’t. But alas, at the 11th row the number of digits is 37+2*φ(11), or 57… 😕

My two favorite channels coming together.

DEEPER INTO THE VAULT WE GO

@OwlRTA

Жыл бұрын

ENHANCE

@ekxo1126

Жыл бұрын

@@OwlRTA i just answered on a comment which was an answer to a comment of an unlisted video that I reached from another unlisted video

@viliml2763

Жыл бұрын

​@@ekxo1126 What video did you come from? I came from a listed video.

@9:47 excuse me but Tim “The Moth” Hein is absolutely an A lister!

@toycobra12

Жыл бұрын

I thought it was the guy from the KFC logo 😂

The second number in the rows of Pascal triangle(the counting numbers) will evenly go into every number in the row IFF the number is prime.

If 1 was a prime number, then the first prime actor would be Sylvester StallONE.

Best video in a long while 🎉❤

Oh darn, part 3 isn't up yet, which means I'm going to close this tab and forget to come back to see the exciting conclusion. :(

@andrewharrison8436

Жыл бұрын

😃I bet you have already subscribed.

@jamesepace

Жыл бұрын

@@andrewharrison8436 Yeah, but if it's unlisted it doesn't show up in the subscriptions list.

So... how many times more I have to refresh the page to see the link to the 3rd part? Are you testing if page refreshes contribute to the views number?

Will the 3rd video be published on one of your channels, so that we'll see it?

This collab is legendary

Actually did research work on Farey sums and polynomials and so on. Wild to see some of it shared here. Feels like a fever dream seeing this presented 🙃

Awesome video!

What is this, a crossover episode? ❤Great stuff as always!

It would be interesting to see how this works in other Bases. Following the totient function of 10, would it break down in a similar manner in duodecimal, or is it merely a trick of numbers merely being close to each other?

@andrewharrison8436

Жыл бұрын

The totient function is independent of base. It depens on common factors (or lack of them) not on the representation of the number.

When adding even numbers (because it's symmetric) to small odd numbers (after the first) it's hard not to hit a prime

Will you upload the third video unlisted?

And the third video is still being edited. But I needed to watch this again anyway. Grant's explanations are so clear and understandable that I keep expecting his channel to come out with a follow-up to his Riemann zeta function video proving the Riemann hypothesis.

3 brown paper videos: you should do 1 on blue paper with him just to complete the inversion

3b1b is a phenom channel. Great collab.

This is an unexpected follow up to Dr. Bonahon's video... Great!!

awesome collab

Part 3 is finally out! Thanks for listening to the like 5 people that were asking for it in this comment section lol :D

According to what you said about it being related to the number of fractions with a maximum denominator, this can compute primes! You just need to check how many numbers are added at each step and for step i, if i-1 numbers were added, then i is prime. I checked up to i=3000 too.

@arandomdiamond2

Жыл бұрын

Not very efficient for calculating big primes though

@TheEternalVortex42

Жыл бұрын

This is just checking the definition of the Euler totient function for primes, since φ(p) = p-1.

@arandomdiamond2

Жыл бұрын

@@TheEternalVortex42 Yes, but I found it interesting since Grant said the "Prime Pyramid" didn't produce primes, and I've never seen primes calculated this way before so I just thought it was cool.

Question about the prime pyramid, would the sequence still break if we used another base? (i.e. Would the same sequence in base 16, break at 16?)

@MichaelDarrow-tr1mn

Жыл бұрын

it's not a base 10 specific thing

This is super cool :) thank you for sharing this with us!

Loving the trilogy!

@backwashjoe7864

Жыл бұрын

I have a reminder set to look for the 4th / "Resurrections" video in 18 years.

Grants always been a great math communicator!

Guys the description changed from "STILL BEING EDITED" to "soon"

NUMBERPHILE I LOVE YOU'RE VIDEOS 💗

My three inventions able to change the all history of mathematics. (1) The Easy Number Theory (2) The Original Remainder Theorem (3) The Prime Pyramid Theorem

It crashed at 10 but what if we count in base 16 and replace 10 by A. Its 1 less digit. Augmenting the base should delay the moment it crashes, is it ?

@aceman0000099

Жыл бұрын

I also wondered if it fails at 10 because of base 10. It may be pure coincidence

@user-qo3qm7ud1d

Жыл бұрын

It does not depend on base of number system!

@kirkanos771

Жыл бұрын

@@user-qo3qm7ud1d That's not our point. Choosing another base may delay the number of iterations before it crashes.

it would be interesting to see the sequence of numbers that are primes that he pyramid skips, and see if they hold any patterns we can recognize

@SgtSupaman

Жыл бұрын

Another comment did the output to just over 100. Here are the skipped primes they came up with: 17, 31, 37, 41, 53, 61, 67, 71, 79, 83, 89, 101

@jurjenbos228

Жыл бұрын

@@SgtSupaman This is not in the OEIS. But the sequence of denominators of Farey sequences is: A006843, and the sequence of numbers of Farey fractions (prime or not) is A005728.

@bad_manbot

Жыл бұрын

@@SgtSupaman nothing quite jumps off the page at me. though it is interesting the differences between the skipped primes from one to the next. 4, 6, 4, 12, 8, 6, 4, 8, 4, 6, 12 way less variability than I expected - though i have a suspicion that this is more due to the "6n+1, 6n-1" nature of primes than anything else. (also given how densely packed they are at the lower end of the number line, as mentioned in this video.)

In this series I saw something I never saw before--veins popping out of Grant's arms. Teach has been lifting!

Papa Grant here to give us some key geometric intuitions

That's the funny addition video! Classic!

A nice mathematician's pause when that second "1/3" is noticed and fixed offscreen for the next section.

In each row ,the most numerous number is the prime but if tie always choose the prime you Know from the previus rows.

Suddenly, it's not unlisted anymore!

The quip about 3b1b being "A list" haha, you certainly are too tho Bradey, I literally started learning math in my 20's because of your channels! :D

But what are small numbers? Are the numbers below 2^2^10 small? The largest prim we found is less than that. Are there generating functions like this that work up to something like 2^2^10? And then fail?

@effuah

Жыл бұрын

There is mill's constant (numberphile did a video some time ago). It generates infinitely many primes, but the problem is that we can't know this constant to a high enough accuracy without also knowing really large primes. If you want an example for a conjecture that works for small numbers (where the small numbers are really large), look at Merten's conjecture. It has some connection to primes.

@michiel412

Жыл бұрын

Just for the record, there's been primes found that are much larger than 2^2^10. 2^2^10 (or 2^1024) has 309 digits, the current largest prime found is 2^82589933 - 1 which has 24862048 digits.

@Anonymous-df8it

Жыл бұрын

@@michiel412 I think that 2^2^10 might be the phone number calculation limit as it can only go to x*10^308.

4:22 so far it is a repeat of the Stern Brocot Sequence and the Funny Fractions video. Which is fine :) . I hope there is more.

lmao, Tim Hein being a very high odd number

Now if I say to some kid who watches numberphile,that Jennifer Lawrence was in a numberphile video, would they believe it😂?

This is the ultimate video

How deep does this rabbit hole go?

7:10 Damn it, it's that Euler guy, again!

This is why you asked for A list and B list actors on Twitter haha

Grant is def a prime number, wish we’d see more of him on his home channel, but pie guy is cute too 😊

neat sleight of hand at 3:47 :)

2:10 As a certain suspender wearing Frenchman would say: "Today, we're looking at frraacctions"

If you use a different base (non-base 10) will the pattern also break once you get to that base?

@isavenewspapers8890

Жыл бұрын

No. The pattern has nothing to do with the digits of the numbers.

@SgtSupaman

Жыл бұрын

How does changing the base matter here? The prime numbers are the same no matter what base you use. For instance, just because 15 in base 10 is written as 13 in base 12, it doesn't magically become a prime number. It's still composite.

Rydberg is watching (finite structure) crystal eyes ...hydrino autopoiesis?

Does the tenth one add up to 33 though? If you count the fact that the number 10 has two digits, you're actually adding 8 instead of 4, making it 37, which is still prime. But there's probably another snag not much further along.

i want the third ep right now pls thanks in advance loving the material

i came up to a problem with similar thing, start with sequence of 111, each next row is the previous sequence as binary number number XOR itself shifted 1 and 2 bits, so 111 XOR 1110 XOR 11100 so 2nd row is 10101, next is 1101011 and so on, find a way to count how many 1 bits are in the nth sequence, i know for n = 2%k the answe is 3, for n=2k it's equal to the answer for n/2, need a formula for the general case

What if you use a radix other than base ten. May be base 14 or base 22?

@divisionzero715

Жыл бұрын

The function is irrespective of base, it shouldn't matter.

If you count the number of digits instead of the number of numbers, you get 37 instead of 33 at n=10, right?

@livedandletdie

Жыл бұрын

no. Because 2/10 is 1/5 and it's already on there, and the same goes for 0/10 4/10 5/10 6/10 8/10 10/10 only leaving 1/10 3/10 7/10 and 9/10 which are the four numbers that would be inserted into the sequence and it would break.

@Anonymous-df8it

Жыл бұрын

@@livedandletdie You insert a 10, 10, 10 and a 10. There are eight new digits.

The mediant of two fractions, huh? Is there a submediant? What about a dominant and subdominant? What's the leading tone of two fractions? What's the supertonic?

Thought this was going in the direction of the Stern-Brocot sequence at first

Soon we shall reach kaizo trap levels of unlisted

Poor Tim!

Well I suppose that one "reason" why you are getting primes at the begining is that this method will never produce an even number, that is guaranteed. It's even weaker than the Paterson method where 2,3 and 5 are excluded as divisors, but it is there :).

I'm only halfway through the video, but does this mean that the gaps between consecutive primes depend somehow on whether the ranks of the primes are prime numbers themselves?

@guillaumelagueyte1019

Жыл бұрын

Oh no the pattern breaks down :(

Thanks .

1:53 MIND BLOWN

That Hollywood celebs analogy was nice.

Third part where?

analyze the wilson's theorem like the pascal's triangle for each n

@Jkauppa

Жыл бұрын

sorry that your brain does not produce clear answers but only mush

@Jkauppa

Жыл бұрын

what do you classify A/B/C as a rule, dont you have all as equal gift

Oh there's no fourth unlisted video 😢

@4:04 Funny addition sign p prrrrrimeee

I wonder how the performance of this stacks up against the Sieve of Eratosthenes?

On the line for number 10 is doesn't break if you count digits, since it becomes 37, not 33.

3Blue1Brown is the GOAT.

Worth pointing out the attention thing that KZread displays skyrockets when the actors are shown on screen lol