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Yes, that's what I thought as soon as I saw that part.

I'm not quite understanding your question regarding the point made at 7:40. Let me illustrate with an example. If there were a prime-counting function capable of rapid computation, and it told us that there are 1,229 prime numbers within 10,060 and 1,230 prime numbers within 10,061, then I would immediately conclude that 10,061 is a prime number. Of course, this number 10,060 could be a very large number.

@@zengg-kc6tl Right. So my question is would a function capable of perfectly predicting that 10,061 is a prime number, or one that can tell us that there are 1229 prime numbers within 10,060 be a proof that Riemann was correct, and therefore be a proof of the Riemann hypothesis? If the Riemann hypothesis is all about identifying primes via analysis and the zeta function, would a constant time function/calculation that could directly compute the prime numbers make the Riemann hypothesis redundant? I will put the question a third way, if someone discovered a direct way to predict any and all primes, what would the consequences be for the Riemann hypothesis? Would it give the person the Millenium Prize?

@@robertferraro236 First of all, I am not a mathematician specializing in the Riemann Hypothesis. Based on my limited knowledge, I believe that a function that can perfectly predict whether a certain number is prime, in the sense of a direct prediction, likely does not exist because the distribution of prime numbers is too random. Both the Riemann Hypothesis and the Prime Number Theorem are indirect predictions of prime numbers. If such a formula existed and could be discovered, it would undoubtedly be the greatest discovery in the history of mathematics since the dawn of human intelligence, and any honor bestowed upon its discoverer would be well-deserved. Regarding your second question, there are many ways to prove a conclusion, and some methods may not be directly related. Therefore, drawing a conclusion does not necessarily imply the correctness of the Riemann Hypothesis. Even if someone were to derive a stronger conclusion than the Riemann Hypothesis, it would not necessarily render the Riemann Hypothesis obsolete. The most important aspect of proof is the new insights, tools, and methods obtained in the process. This is akin to Newton's classical mechanics and Einstein's theory of relativity; while relativity is clearly more powerful than classical mechanics, no one claims that classical mechanics is redundant.

This video, by the way, is the best explanation out there about the RH. Your answer to my questions is well explained too. Now I get it.

Great question

I think that’s the last number for graham’s number but we do not know the any of the numbers for tree 3

Then you could be remembered throughout history; this is a lifelong belief for many people.

Nobody knows how large sscg3 is.

It is said that SSCG(3) is larger than tree(3tree(3)…) repeated tree(3) number of times.

New mathematical tools and new ideas are needed. If we continue with the current approach, even if we prove to 100%, it doesn't necessarily mean we have proven the Riemann Hypothesis (RH).

@@zengg-kc6tl If we _disprove_ a lot of conjuctures that today seem very likely - yes.

Fight the machine!

Agreed. It looks really great, but I get very badly thrown by the machine-generated sound-track. It's very distracting when the intonation is so bad.

@@simlee6177 And how do we know that it wasn't scripted by AI, with the video clips pulled and assembled by AI? If we aren't experiencing that at this moment, you know that we will be very soon. And then what will we have? A bunch of human beings being taught about their world by machines, as the machines see fit.

Sure, sure, my apologies - I didn't mean to say that it wasn't generated by AI nor that I wouldn't mind if it was. The first is possible, and the second is also cause for hesitation and resistance. I only meant that for me, the "robot voice" was what struck me most and what bothered me most. And that robot voice actually points all the more to the probability that the whole thing was AI generated. (Though I have to add that these machine generated narrations have improved a lot in the last 3-5 years - before that I used to detect it immediately, these days it sometimes takes me several minutes before I realize it. In this particular video, it's the reading of the formulae which gives it away, IMHO.)

Good point. Not worth 30 minutes...

10^10 is 10 billion

@Nerdfr126 American billions, not metric billions.

@@FebruaryHas30Days in metric: 10 thousand million

@@C-dive_21 it's the Greek letter phi

if you wanted to, you would need to googologise the f and phi, maybe with some [10,10,10] (birds extended array notation) with some editing, and the f phi is in that BEA notation

Your expectations are too high😂 At least among the people I can reach, no one can answer your questions. I even wonder if there’s anyone who can provide a quantitative answer to these questions-it might only be possible to give a qualitative answer about which one is larger.

There's a good video showing what a googol dice looks like stacked up. The size is absolutely insane. And that's a googol, which might as well be zero compared to a googolplex, which might as well be zero compared to Graham's #, which might as well be zero compared to Tree(3)

It’s fine, we all make mistakes, also, How did you find the lower bound limit at the end?

@@zengg-kc6tlokay, also, theoretically, how would you find an *upper* bound limit for TREE(3), or a lower bound limit for TREE(4)

It's all cool, great video

You shouldn't be making videos.

Yes, some AI was used.

AI is not omnipotent, and the vast majority of work requires human involvement.

@@zengg-kc6tl It sounds artificial, it looks artificial. When I leave here, I will click "Do not recommend channel." Interesting topic, but do it youself; don't use AI generated content.

I can't even understand G2.

This proof method is indeed epic. I find it truly elegant and have decided to analyze it.

"Tree (3)" is a game where players draw "trees" using three different colors, with each color representing a unique tree. The rule is that subsequent trees cannot incorporate the shapes of previously drawn trees. How many different ways are there to draw these trees

@@zengg-kc6tl So TERR is a typo?

Embarrassing, there was indeed a spelling mistake, I didn't notice it, and I can't change it now 🤣🤣

@@zengg-kc6tl This is why I asked. There is a tree(3) with small letters, then the famous TREE(3), and I thought that TERR[3] is something else in-between.

Thank you for liking this video.

I can't find the corresponding information, and I don't know how to approximate SSCG(3) using TREE3.

Yes, so I wrote approximately equal to, and the error might be very, very large.

It is in fact way larger, nobody can comprehend it

Thank you for your comment, I will make more and better videos.

Thank you for your correction. These numbers are too big to imagine, even for G1.

​@@zengg-kc6tl tbh G(G1) is already larger than the false wikipedia entry (should be corrected) for TREE(3)'s lower bound.

I thought tree(3) was finite? Does not seem like it can be within transfinite ordinals in size and still be finite. Id like to know the explanation.

@@patrikwilliam-olsson3390 transfinite ordinals are not actually infinite "values". At this stage of large numbers we stop thinking of them in terms of actual values but rather how fast they scale (kind of like big O notation in computer science). When you add to the ordinal it basically means "we've reached our limit of meaningfully describing this level of recursion and we're moving onto the next"

@@lowdefinition4250 So your argument is that it is not a finite number then, tree(3) that is. Because the ordinals you refer to are not finite. I am not a professional more of an enthusiast so i might be on slippery ground here. However, i have not Come across anyone describe uncomputable numbers as being beyond finite. They grow faster than anything computable but still finite. Therefore not comparable to transfinite ordinal sets. Are you reffering the growth rate of the tree function that is something different i dont dare to engage in atm.