The floor functions are doing a LOT of hard work here
@GERARD590
5 күн бұрын
Can't you just take the nth root instead of raising it to 1/n? Also (cos(any value))² is just cos²(any value)
@EricRowland
2 күн бұрын
Yes, those are different notations for the same operation.
@draido-dev
11 күн бұрын
noticed this pattern while solving project euler #443, lovely video!
@runway4970
16 күн бұрын
I love the fact this is a thing that somehow make sense
@soyezegaming
16 күн бұрын
1 is the 0th prime
@kroon275
18 күн бұрын
Its like theres a secret language in maths that we are just learning about but dont quite understand. Maybe intelligences far greater than ours are waiting for us to crack the code before they come say hi or something lol
@miloszforman6270
18 күн бұрын
There is nothing scecret about math, or is it? Unfortunaly, it tends to get complicated at some point so that many cannot follow pace. But that's the same in technological fields, and worse in physics.
@jamesmoore8994
19 күн бұрын
The exact equations that define the Prime Number Sequence were found and proven 11 years ago: kzitem.info/news/bejne/o3qL3GSBs5yGoWk
@kpaasial
27 күн бұрын
0:44 Just sum together 2^1000 terms to get the 1000th prime number. It shouldn't take that long, right?
@debmalyalodh1
29 күн бұрын
Welcome back
@susa4727
29 күн бұрын
Great video and explanation, loved it. I'm a mechanical engineer but I also love computer science and math so this video was perfect for me
@JeremyCaron
Ай бұрын
That's not a formula, that's a program
@gigachad6844
Ай бұрын
Can't we use Sieve of Eratosthenes instead for prime detection?
@heathertilton3056
Ай бұрын
1/3=⅓=0.33333333333
@miloszforman6270
28 күн бұрын
No. 0.33333333333 = 1/3 - 1/300000000000 according to "Windows Calculator" (calc.exe).
@heathertilton3056
Ай бұрын
1÷∞=0.00000000000000000000...1 there is infinity zeros
@miloszforman6270
28 күн бұрын
Are there numbers which have a decimal expansion with infinitely many zeros, followed by a 1?
@Honorary_Redneck
Ай бұрын
Alternate/parallel/multi universes require zero actual evidence but are treated as a forgone conclusion..cause math can literally be made to say anything you like.
@d.paradyss8791
22 күн бұрын
Exacto
@Honorary_Redneck
22 күн бұрын
However IF other universes existed they would still be bound by the law of conservation of energy and so there would not be a lot and they would be temporary.. constantly being recycled into either new universes or a prime universe. I.e. Parallel universes would exist long enough to solidify the events that caused them with their prime being the constant. This would explain "Mandela effects" as the prime universe and parallel universe balance when recombined. The reason people would even remember events differently is because the core memory of humans is extra spacial via the pituitary gland.. information (can't be destroyed) is thus superpositioned and thus outside the "rewrite" function of universe recombination. This storage of information outside time-space via superposition allows echos of alternate events to be accessed
@d.paradyss8791
22 күн бұрын
@@Honorary_Redneck Tengo algunas teorías algo diferentes pero aprecio profundamente tu punto de vista, podríamos contactar por algún sitio para conversar?
@uggupuggu
Ай бұрын
how is ...4444+1=0? 14:59
@miloszforman6270
Ай бұрын
In the 5-adic numbers, or even in standard numbers denoted in base-5, we have 4 + 1 = 10. - Did you even notice that 14:59 handles the case of 5-adics?
@-PeterAndrewNamoraMarpaung
Ай бұрын
C.P Willans = Calculating primes Willans
@henrikljungstrand2036
Ай бұрын
The floor function is not a continuous function for real numbers. Therefore it is to be expected not to work properly in any algorithmic implementation for non-integer rational or floating point numbers close enough to an integer.
@trapkat8213
Ай бұрын
Wow. Brilliant work and brilliant presentation.
@monkeymathematician5896
Ай бұрын
What is said from 8:04 prevents from looping over all values of a cluster and sets its boundaries. It also means that the last value's index of the cluster is enough to describe it and averaging the values or the indexes could be unnecessary. It also says that there might be something hidden in the gap between two clusters. This saved me weeks, maybe months of work and much CPU time. Deserves the Fields to me. Thank you Professor 😁
@ght0076
Ай бұрын
Me realising sums are basically for loops and floors are basically if statements 🤯
@jalma9643
Ай бұрын
This feel like mathematic in a programming language because of how it work with 0 and 1
@BurningShipFractal
Ай бұрын
It still seems to work for n = log base 2 of 3 Or other numbers that can be expressed by log base 2
@hootowlme
Ай бұрын
I don’t get it. We don’t use it just because it’s too slow? But it DOES give us the nth prime?
@_bhargav229
Ай бұрын
Yes it does, it only relies on Wilson's theorem being true.
@playgpgame
Ай бұрын
A new theorem on primes kzitem.info/news/bejne/06Cj3aCBhJOqd5wsi=z2aSMITtVvQfWE5G Using the product of consecutive odd numbers (rather than the factorial product), the theorem provides a necessary and sufficient condition for whether an odd number n ≥ 9 is prime.
@bruce_invincible
Ай бұрын
my brain got rewired into spaghetti... gotta watch this again :P
@EliasMheart
Ай бұрын
Most common is 3, mostly it's every other prime. (Though it differences get larger further down) If there's a 5, it's followed by a 3. (Could be an artifact from the previous one) ... Otherwise, not sure.
@hiramanchaudhari4485
Ай бұрын
You just copied 3Blue1Brown
@miloszforman6270
Ай бұрын
It covers the same topic, but I would not say that it is a copy. You might watch this video, and the one by 3B1B, and the one by Veritasium altogether, and this may be helpful for understanding, as each one has a slightly different point of view.
@bijousmith1021
Ай бұрын
@15:30 has the last word been written on this? Summing divergent series in the Reals can be analytically continued, and does anyone know for sure there is not some divergent series that sums to _i$? (Cesàro, Abel, or Ramanujan summation?) justaskin'. Seems no less contrived than p-adics.
@miloszforman6270
Ай бұрын
_"@__15:30__ has the last word been written on this?"_ What's "this"? I can't see a context relating to the video. And what's "_i$"?
@aperinich
Ай бұрын
It's a system BASED ON THE REAL NUMBERS. It's not an alternative, it's a subsidiary.
@miloszforman6270
Ай бұрын
We'd better say that it is based on the rational numbers, as by far not all irrational numbers are part of the p-adic numbers, if any. And of course, the p-adic numbers are not an alternative to the real numbers. There are probably not many applications in the real world. There might be some in connection with encryption theory, but I'm not sure about that.
@aperinich
Ай бұрын
sorry you're right in correcting on rational vs. real, as obviously there are real numbers which have no right-most decimal value@@miloszforman6270
@aperinich
Ай бұрын
so 10-adic is like some inverse real log-10 base. I damn well hope we get to some useful applications.
@aperinich
Ай бұрын
When you use real addition, it proceeds from right to left too - just in a real and geometric sense. Who adds from the left? WTF??!
@aperinich
Ай бұрын
You can't rebuild your intuition.
@aperinich
Ай бұрын
Why isn't 78000 ten-adic = 78/1000 ? Why is it equal to 35000 ten-adic? If it's just the trailing zeroes in the value, then why represent it as a fraction at all? What a crock of shit!
@miloszforman6270
Ай бұрын
What are you talking about? 10-adic 78000 isn't equal to 10-adic 35000, or is it??? Perhaps you have failed to notice the "absolute value strokes" "|...|" ? And yes, |78000|₁₀ = |35000|₁₀ = |999000|₁₀ = 1/1000, where 1/1000 = 0.001 is a genuine _real_ number, as absolute values are always non-negative real numbers.
@aperinich
Ай бұрын
My question was based on the claim in the video... I may have gotten the notation wrong, but if you watch the video and the clear point I'm referencing, ... I'm sure you;ll get what I mean. The real point I'm driving at is why represent these concerns in the same notation as a fraction. They aren't rational equivalents. 78000, 35000 and 999000 aren't equivalent . It's not that I failed to notice the absolute value strokes, I don't see their relevance nor do I see why these are notated as rational fractions when they are only related through the facet of their 1/1000-ness. I find the whole thing annoying and not useful in terms of notation @@miloszforman6270
@aperinich
Ай бұрын
all of the examples are positive integers, for which the absolute value gate does nothing, all positive values are positive values. That is self-evident. So is the absolute value gate used to represent the adic operation, or does it actually have anything to do with absolute value? @@miloszforman6270 Maybe the examples in the video could have been better in terms of explaining why the notation is used, and perhaps an example of an adic operation being done on a negative value to show if/how absoluteness of value even comes into the matter.
@miloszforman6270
Ай бұрын
@@aperinich There are no negative numbers in the p-adic numbers. _"So is the absolute value gate used to represent the adic operation"_ "Gate"? Sorry, I can't understand this kind of complicated language. These p-adic numbers are kind of weird, and they are abstract. It took me quite a time - and several repetitions - to understand what this is all about. And actually I do have a mathematical background. If you want to understand all of this, you have to proceed thoroughly, and you can't expect that it's easy. There are other videos on YT giving introductions. You may try those of Veritasium and 3B1B. There is also a lengthy Wikipedia article. Unfortunately, such Wikpedia articles tend to be very concise and shortform, not well suited as an introduction. Nevertheless, they are a valuable support.
@aperinich
Ай бұрын
Yeah I absolutely devalue Wikipedia Mathematics! I think for now I will stick to the practical, and the syllabus I'm studying in Mathematics before going into complex analysis and still that before p-adic anything, as I want to fully formalise my maths (yes, we pluralise 'math' in Australia) a step at a time .. Anyhow it's not that this is all that complicated, I'm just previously entirely unfamiliar with it before seeing this video, and still haven't yet seen or heard of one useful application.. so I'm curious and annoyed @@miloszforman6270
@TheAscendedMaster
Ай бұрын
Numbers are an idea that isn't real and never will be. Of course they will converge or match or find a series or set. You have to realize that the only options for these numbers you are giving are 0123456789. That's it. No matter what length,size or randomization eventually with such few choices they will randomly line up.
@miloszforman6270
Ай бұрын
This sounds quite lika a pointless, or nonsense comment. Maybe I'm missing the hidden deeper meaning.
@nyxcode2818
Ай бұрын
Reminds me of Tupper's self-referential formula from 2001. When graphed, you get a 16x106px image of the formula. Basically a quine in the language of math.
@alaazingi5784
Ай бұрын
what programming language do you use? Math++
@nicopb4240
Ай бұрын
What a beautiful video! Very well explained and illustrated, thank you 🙏🏻
@Adrian-me4qz
Ай бұрын
That trick with pi and cosine is insanely clever...
@betanapallisandeepra
Ай бұрын
Awesome explanation and very nice formula… Initially I thought this formula seems so complex and how did he get to that. But after listening to the explanation of the breakdown it’s easy to understand how the formula has been developed… good job… 😊
@dcterr1
Ай бұрын
Incidentally, for those interested, a few months ago I discovered the formula 4*.5!^2 for pi, which involves just six characters limited to the decimal digits 0 through 9, the arithmetic operations +, -, *, /, factorial notation (!), and exponentiation (shown as superscripts, which I didn't do here!).
@dcterr1
Ай бұрын
You make a very interesting point at the end that our functional notation involves computation in disguise, so it seems that with rich enough arithmetic notation, which I assume we already have, we could in principle write down a formula for any computable quantity, though it might be completely useless! Has any result like this ever been proven? If not, I wouldn't mind working on this problem!
@dcterr1
Ай бұрын
I learned a long time ago that there are several formulas for generating all primes or only primes, but that they're all useless like this one in the sense that they either involve the Sieve or Eratosthenes or less efficient algorithms for computing primes in their formulations.
@JustAnotherSomebody001
Ай бұрын
This reminded me of a Phyics problems regarding counting the no. of collisions between the blocks of mass 'm' and '(100^(n-1))m' (and the no. of collisions between the lighter block and the wall used for rebounding) to calculate the first 'n' digits of π. By the way, your explanation regarding the formula was great (couldn't understand anything initially, but slowly grasped on the ideas used here).
@j.jwhitty5861
Ай бұрын
Excellent presentation of p-adic Numbers, the only time I have actually heard of them being used in the real word was by Computer programmers using Quantum Computers for cryptographic security and I honestly have no idea how successful them have been.
@simongross3122
Ай бұрын
Excellent. Remarkably clever even if it is "useless" as you say.
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