Even better, he said 'to the absolute limit' to make it more complex. Is that good enough for a total beat-up?

From the Inner Mind, to the Outer Limits!

That was a Parker Square of a joke

@@tejnadkarni131 Ah, I feel like you're a traitor, even though I do like Numberphile too

Best channels for insomnia so relaxing

The expressions 6n +/- 1 produce all prime numbers greater than three, and many more composite numbers. If we knew exactly where the composite numbers would appear in these sequences, we could infer the location of all of the prime numbers. Am I understanding this correctly? Of what use would this be to anyone?

"Take the differences between 1 and the square of reciprocal of every prime number. Multiply them out to each other and take the reciprocal of this product. Multiply this reciprocal by 6 and square root the result. The value thus obtained is the ratio of the distance all around a circle to the distance across it".

@@aaronleperspicace1704 something interesting about this is how mystical pi seems when it is classically defined in terms of circles. No wonder hardcore analysts think of pi as defined based on infinite series and do not appeal to geometry.

By all means it's a non-prime.

@@viharsarok So, it has other factors, beside itself and 1 (which is itself)? I’d like to know more about these mysterious factors. 🤔

Welcome to Nz, hope you have an enjoyable stay

Please do some videos on fractional calculus!

+Josh I'll put this topic on my list of things to ponder :)

Mathologer I'm not sure whether your proof (with conclusion at 5:16) is complete. Is that really a contradiction? Even if one function is bounded above by another, couldn't they still converge to the same value, as long as the difference between the sums converges to 0?

You should consider doing a video taking infinite products to infinite fractions (which is again due to Euler), especially condiering you already have videos on infinite fractions you can reference.

"especially how the prime product connects to the zeta function. That has always confused me - and I was probably too lazy to look it up - but that it's so simple is just ..beautiful in a weird way." Ah, me too, I'm glad that I understand it now

I solved the Riemann Zeta function! I posted the solution, check it out!

I solved and proved the Riemann Zeta function. I just posted the solution check it out!

Please tell me how it was relevant! I'm doing math and physics research

Glad these videos work for you exactly as planned, and thank you very much for saying so :)

If only I had a bit more time. It would be great to be able to make more of these videos :)

David Herrera Loma?

Glad you like it :)

+Elie Simsch This problem is called the Josephus problem :)

Great, looks like "mission accomplished" as far as you are concerned :)

I like this video a lot. At @9:46 the video seems a bit unclear of what is required to show for a second time that there are infinitely many primes, using equation: pi^2 / 6 = 1 / ( (1 - 1 / 2^2) * (1 - 1 / 2^3) * (1 - 1 / 5^2) * (1 - 1 / 7^2) * ... * (1 - 1 / prime(max)^2) ) with an assumed maximum prime number, prime(max). On the right side is a rational number, and it would follow that pi^2 is rational. But that pi^2 is irrational is a stronger statement than pi being irrational, like the square root of 2 is irrational, but its square, 2, is rational. Therefore, it's not enough to show that pi is irrational, which is difficult enough, but we would have to show that pi^2 is irrational for showing that there are infinitely many prime numbers. I personally find the proof using zeta(1) more beautiful.

😂 No, its ur chance bro.

I looked at this a while ago, but from your comment it would seem that there have been some new developments. Do you know of some good references? I should really do another Rubik's cubed video sometime soon .... :)

Well I learned most things from this video series on youtube: kzfaq.info/sun/PL0yL0AZiHw10Kx5um2l4MdOAICtRqJwac But this video series only explains how to apply some techniques. I came up with explanations for the techniques myself and you probably could too, but I later found this pdf: fmcsolves.cubing.net/fmc_tutorial_ENG.pdf This pdf goes more in-depth and has some explanations for the techniques it discusses as well. It also describes even some techniques not discussed in the video series. I do think the video series is still very good and will probably help more with visualizing than the pdf, even if the pdf has pictures and you can follow what the pdf is talking about by applying examples to one of your own Rubik's cubes. But I also recommend reading the pdf, even if it is pretty long, because this stuff is pretty interesting.

It doesnt? Assume your statement is true, then: A = 1/1 + 1/3 + 1/5 +... B = 1/2 + 1/4 + 1/6 +... Let C= 1/3 + 1/5+... D = 1/4 + 1/6 +... By your statement C>=D. A -1/1 = C B -1/2= D A - 1/1 >= B - 1/2 A >= B + 1/2 A > B

1-π^2/12?

Yep!

@Catharsis it's 1 - the alternating sum for n=2 shown in the video

kzfaq.info/get/bejne/j9t5fM1915zahXU.html (he made this - it addresses some of it)

this is a good point, 6/pi^2 is just the limiting behavior

כמה משעמם לך אחי

dmagen1994 אותה כמות שמשעמם לכולנו 🙂

lol, made the exact same mistake in a math exam. I also assumed 28 was dividable by 3

Yeah

Like I want it to be 69 so I am replying

Euler later did find a fairly simple derivation that gives, for even numbers only, the value of zeta as a rational number times that power of pi. In other words, zeta(102) is an explicit rational number times pi to the 102 power. It was a bit of mathematical good luck that left Euler the possibility to turn up the value for zeta(2). I can't imagine that Euler, and other mathematicians since, haven't done more than ponder whether something like it exists for odd numbers, like 3, but I have never seen any such natural thought expressed in print, pro or con. From that, I take it that whatever they have done shows no indication that it is a rational number times that odd power of pi, or any power of pi. It is possible, though, that professional mathematicians consider such speculations as the realm of crackpots, and do not care to be classed as such, and that explains their reticence. However, sometimes it is mentioned that, not so many years ago, it was proved that zeta(3) is irrational. The nice formula for even values of zeta can be turned into a formula for odd powers, but it would involve the odd Bernoulli numbers, which are zero (beyond 1), and powers of i, which would make zeta for odd numbers seem to be both imaginary and 0. How could you fix that? It is the kind problem you know Euler would love.