Twin Proofs for Twin Primes - Numberphile

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27 сен 2024

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Комментарии : 631

@jdmarino 2 года назад

Ben Sparks must be a great math teacher. Energy, big smile, almost childlike wonder.

@blokin5039 2 года назад

Are you angry 😠

@benjaminlehman3221 2 года назад

Hold on, He’s British. It’s maths teacher 🤣

@andrebenites9919 2 года назад

He does Spark some energy in his explanations... I'm sorry for the pun. I'm a math teacher, it is stronger than me.

@Debilitator47 2 года назад

He reminds me of my algebra teacher, Mr. Burke, but in a negative way. Mr. Burke was constantly putting down. Make a mistake, have an eyeroll and a question about how you ever made it this far. he did not inspire. My next teacher, Mr. Hughes, he was much more of a teacher, and I landed my first A in math class, not to mention awakening an interest in learning and math specifically.

@Wool_Scarf 2 года назад

The mod9 being equivalent to digital root is insane to me, despite being such a simple proof

@leamanc 2 года назад

I think the most simple proofs can be the most mind blowing!

@Syrange13 2 года назад

It's actually just the more general version of the well-known divisibility trick.

@ssvis2 2 года назад

Ah, but that only works in Base 10. There are equivalents in other bases (ex. 8, 16, etc.). The same approach works in using mod [Base - 1] at which point you'll realize that our representation of written numbers is largely arbitrary and you can represent them in significantly different ways. What's important is how a number is assembled (sums, multiples, etc.), not how we write it. A prime is a prime regardless of representation.

@LysterSC 2 года назад

I agree, this proof is so elegant

@courtney-ray 2 года назад

@@Syrange13 exactly! If you know all multiples of 9=9 it’s not surprising. I learned that on Square One TV as a child. But it’s also nice to learn the “elegant” way to prove it 🙂

@GUIHTD 2 года назад

"Proof by thinking" is now my favorite kind of proof.

@KayvanAbbasi 2 года назад

I love every episode of Ben Sparks on Numberphile.

@GasparLewis 2 года назад

If you "want the 8 to appear" naturally, define your primes as 3k+2 and 3k+4 and multiply out to 9k^2 + 18k + 8. Of course, the demystifying bit is that generated pairs that AREN'T twin primes also yield 8 as a digital root anyway. For k=7, 23 x 25 = 575, 5+7+5 = 17, 1+7=8.

@walterkipferl6729 2 года назад

That is often the case tho, with the nice patterns in primes. There is a Matt Parker on numberphile video about prime squares mod 24, that also has that same problem.

@hierismail 2 года назад

Part of the proof was that of three integers in a row, one of them can be divided by 3. In the case of n-1, n and n+1 where the first and last are primes, it has to be n that can be divided by 3. Could a similar conclusion be said about n, n+2 and n+4? Or would you 'move the n back' after the first step? (Sorry, English is not my first language)

@kainotachi 2 года назад

@@hierismail For n+2 and n+4, the number in the middle would be n+3. If n is divisible by 3, then so is n+3, so that doesn't really change anything. For any set of three numbers in a row, one of them MUST be divisible by 3. So if n+2 and n+4 are both prime, and therefore not divisible by 3, then the one in the middle must be, just like in the n+1 and n+3 example.

@hierismail 2 года назад

@@kainotachi oh of course! The answer was right there, thank you

@petertaylor4980 2 года назад

@@hierismail, if k is not divisible by 3, exactly one of n, n+k, n+2k is divisible by 3.

@Wecoc1 2 года назад

This is a nice way to check if two known primes are twin. No, wait-

@delofon 2 года назад

I mean, you're not wrong.

@Wtahc 2 года назад

@@delofon are u daft

@StefanReich 2 года назад

😂

@oz_jones 2 года назад

@@Wtahc Are you?

@Wtahc 2 года назад

@@oz_jones nop

@rudranil-c 2 года назад

I like Ben Sparks the best among all the brilliant mathematicians who appear on this channel. I still cannot forget the chaos theory video and the one with the mandelbrot set from Ben. Thank you.

@445supermag 2 года назад

Not only is the number between twin primes divisible by 3, it also has to be even, so its always divisible by 6.

@ConsciousExpression 2 года назад

Every number is divisible by 6! All you have to do is put a slash between the number you want to divide and the 6 and voila! e.g. - 1/6 (jk, I know what you meant)

@mmmmmmmmmmmmm 2 года назад

@@ConsciousExpression But that's 6, not 6! = 720

@ConsciousExpression 2 года назад

@@mmmmmmmmmmmmm Drat! Foiled in my pedantry!

@sp00g37 2 года назад

@@mmmmmmmmmmmmm but 1! and 0! are equal to 1, and that seems like witch craft

@locomotivetrainstation6053 Год назад

Which also means all of the numbers between twin primes are abundant since 6 is perfect, the only exceptions are 4 and 6

@thegreatchrispy 2 года назад

Man, I've loved modular arithmetic ever since I first learned about it. It opens up so many unexpected doors in maths.

@hybmnzz2658 2 года назад

Math olympiad contests feel like 90% applied modular arithmetic.

@freshrockpapa-e7799 Год назад

Revolving doors? (:

@goyalayush55 2 года назад

Expect the pair 3 and 5 ofcourse!

@MrCheeze 2 года назад

I love that Brady immediately tried to make sure it wasn't just a property true of all primes! Very easy thing to miss, he's clearly used to mathematical thinking now.

@General12th 2 года назад

HE'S LEARNING! ~James Grime

@radadadadee 2 года назад

At first I thought "isn't this a property of any two numbers that differ by 2?". Turns out it is not.

@vigilantcosmicpenguin8721 2 года назад

Brady's conjecture may have been false, but it was an important moment.

@CDCI3 2 года назад

@@radadadadee same

@samevans4834 2 года назад

Should've known the TAS researcher extraordinaire was also into recreational math

@MCPhssthpok 2 года назад

The second proof tells you that the product of *any* pair of numbers that are either side of a multiple of three is congruent to 8 (mod 9). E.g. 14×16=224=8 (mod 9). You get the twin primes result as a bonus since they are always either side of a multiple of three.

@anttheknee1 2 года назад

You can use the same proof to prove that all cousin primes (4 apart) will have a digital root of 5, and sexy primes (6 apart) greater than 7 will have a digital root of 4

@ronaldmullins8221 2 года назад

We need a Numberphile extra on these just for the fun of it

@idontwantahandlethough 2 года назад

All in favor of making "sexy primes" an official classification? I'm definitely on board.

@tobiaswilhelmi4819 2 года назад

@@idontwantahandlethoughIf twin primes are 2 numbers apart, and primes 4 numbers apart are cousins I think primes 6 numbers apart should live in the same valley following the same logic. That would make them Saarland primes in Germany, and maybe Idaho primes in the US? *running away

@ZipplyZane 2 года назад

@@idontwantahandlethough I'm pretty sure it's already official. At the very least, it's appeared on Numberphile more than once.

@Anonymous-df8it 2 года назад

You can actually go further! All primes >3 are in the form of either 6k-1 or 6k+1. This means that: with twin primes: (6k-1)(6k+1)=36k^2-1; they give 35 mod 36 with cousin primes: (6k+1)(6(k+1)-1)=36k(k+1)-6k+6(k+1)-1=36k(k+1)+12k+5; these give 5 mod 12 with sexy primes: (6k+1)(6(k+1)+1)=36k(k+1)+6k+6(k+1)+1=12k+7 or (6k-1)(6(k+1)-1)=36k(k+1)-6k-6(k+1)+1=36(k+1)-12k-5; they give 7 mod 12 etc. This means that in senary (my favorite number base): twin primes give something that ends in: 55 cousin primes give something that ends in: 5, 25, 45 sexy primes give something that ends in: 11, 31, 51 etc. A nice reason to like senary (there are many more, but they're irrelevant to this discussion)

@SaturnCanuck 2 года назад

That was lovely. I love primes. More primes. The "3" between twin primes was awesome

@TheImpressionist235 2 года назад

Actually it's 6, because the number has to be even, too, but it doesn't affect the proof.

@SaturnCanuck 2 года назад

@@TheImpressionist235 Thanks for clearing that up

@locomotivetrainstation6053 Год назад

@@SaturnCanuck and 6 also means every number between twin primes would be abundant except for 4 and 6

@bananatassium7009 2 года назад

always love the ben sparks episodes, i knew some of the ideas behind it but the way he puts the information is always so interesting

@__mads__ 2 года назад

This was so much fun. In uncertain times, it’s a relief to find that numbers remain reliable.

@RJSRdg 2 года назад

Until you add all the positive integers together.... ;-P

@blueskyla7978 Год назад

Interesting in that the number 8 has always, like ALWAYS, been my favorite number.

@maxwellhosler4918 2 года назад

got a bit overexcited, I thought we had gotten a twin primes proof this is still weird and cool though!

@cosmo1248 2 года назад

So did I unfortunately

@trinityy-7 2 года назад

same here

@LegendaryFartMaster 2 года назад

An informed numberphile viewer might remember another video, "Squaring Primes" from Matt Parker here. And indeed,in both cases, the first proof was an exhaustive one, while the second proof was the "prettier".

@biquinary 2 года назад

There's also casting out nines with James Grime!

@falknfurter 2 года назад

The simple identity a^2 - 1 = (a-1)(a+1) is indeed a powerful idea in quite some proofs in number theory.

@monkeybusiness673 2 года назад

@@epsi Well, at least it wasn't a "Parker square" of a solution ;-)

@whitey.mp4676 4 месяца назад

@@monkeybusiness673😂😁

@tristanc6967 2 года назад

12:06 "We proved by thinking..." Is such a great line!

@RAG981 2 года назад

Twin primes are of the form 6n-1, 6n+1. Multiply then gives 36n^2-1. Digit sum of 36 is 0. 0 times n^2 digit sum is 0, so digit sum of 36n^2 -1 is -1, which is 8

@RAG981 2 года назад

If you do not believe all primes are of the form 6n-1 or 6n+1, think about 6n+2, 6n+3, 6n+4 and 6n+5 which is back to being of the form 6n-1.

@reddcube 2 года назад

So you can pick any integer divisible by 3 and take the 2 numbers on either side. 123,456,788 and 123,456,790

@guepardiez 2 года назад

So this actually proves that the digital root of the product of two integers, prime or not, separated by two is always eight if neither of those two integers is divisible by three.

@theadamabrams 2 года назад

Yes, prime-ness is not necessary, only not-divisible-by-3-ness. Also, your statement can be "iff": digitalRoot(n * (n+2)) = 8 if *and only if* both n and n+2 are not divisible by 3.

@guepardiez 2 года назад

@@theadamabrams Nice!

@RiseUpUNAFRAID4614 2 года назад

I miss my twin brother, he passed several years ago 😢. I'll see him soon.

@AlisterCountel 2 года назад

Every time I watch one of these, I feel obligated to figure out the proof before we arrive at it. I ended up with the algebra proof and was satisfied, but humorously, hadn’t even considered just checking the cases mod 9!

@pepega3344 2 года назад

I did the same when they first introduced twin primes years back. I proved that there are infinitely many as an exercise. Sadly the proof doesn't fit in the youtube comment section :(

@hvok99 2 года назад

If 'p' is a prime number bigger than 3, then (p^2) -1 is always divisible by 24 with no remainder. I think numberphile has touched on this before, but this video has inspired me to investigate if another Modular arithmetic fact is available along that line if thinking 🤔

@patrickwienhoft7987 2 года назад

p = 6k+1 or 6k-1 for all primes p except 2 and 3. Thus, p² -1 = 36k² + 12k = 12 * k * (3k+1) If k is even, then 24 | 12k. If k is odd then 3k+1 is even and thus 24 | 12 * (3k+1)

@gcewing 2 года назад

So to reduce a number mod m, all you have to do is convert it to base m+1, find the digital root, and convert back!

@mytube001 4 месяца назад

I just realized who Ben reminds me of. Anthony Quayle! I've been thinking about it every video I've seen, but only now did it come to me.

@ffggddss 2 года назад

The product of twin primes > 3, is congruent to 8 mod 9. Is this true of any twin primes (other than 3 & 5, of course)? Yes, because it's true of any pair of integers that bracket a multiple of 6; and all twin prime pairs do that. (6k+1)(6k-1) = 36k² - 1 = 9(4k²) - 1, which is congruent to -1, and therefore, to 8, mod 9. The reason twin primes always flank a multiple of 6, is that any pair of integers that differ by 2, must include a multiple of either 2 or 3, unless they are ±1 mod 6. Which is also why (3, 5) are exceptions to the twin-prime-product rule. (A multiple of 3 can't be prime unless it is 3 itself.) Fred

@VietVuHunzter 2 года назад

This bring back so much memory to me. Modulo arithmetic was fascinating to me when I was in middle school.

@bosstoober8782 2 года назад

you can go one further, since the middle number must also be even, the product of twin primes is one less than a multiple of 36 (6k+1)(6k-1)=36k^2-1

@HebaruSan 2 года назад

"... just kidding, I wrote a different number under each corner of the paper. Gotcha!"

@TechnoHackerVid 2 года назад

I've a question about the mod 9 digital root proof: The digital root of 9 is 9, but 9 mod 9 = 0. Is it treated as a special case or am I grasping it wrong?

@pwhqngl0evzeg7z37 2 года назад

It's a special case; see my comment (coming soon)

@willarn1 2 года назад

Great video and guest.

@moonshinepz 2 года назад

I'm 64. The algorithm suggested this for me after I had been researching my dyscalculia. 🤣 I really enjoyed the video though. This guy must be a great teacher.

@eabeeson Год назад

“Proved by thinking” -Ben Sparks

@samr9408 2 года назад

The second proof makes it clear that this is a property of any two numbers which are one more and one less than a multiple of 3, prime or not. For example 20 and 22 have this property.

@tourajtayebi2189 2 года назад

@0:28 I like his honesty

@martinepstein9826 2 года назад

Great video. Ben is slightly mistaken at 13:05. As he showed, the product is 9k^2-1. To get +8 you have to rewrite it as 9(k^2- 1)+8

@Syrange13 2 года назад

The moral of the story, to me, is that this is a property of any two numbers on either side of a multiple of 3, and twin primes (other than 3 and 5) are a subset of those pairs of numbers.

@tobiaswilhelmi4819 2 года назад

You can even generalize a little bit further: given that the primes are odd, the number encircled by them is also a multiple of 2, which leads to the statement that you can only find twin primes around multiples of 6.

@zinxys 2 года назад

Better generalization is all primes greater than 3 are of the form 6k ±1

@Leeisateam 2 года назад

The product of twin primes (excluding 3 and 5) is also equivalent to 35 (mod 36). Proof: All twin primes other than 3 and 5 are in the form (6n - 1, 6n + 1) where n is a positive integer. (6n - 1)(6n + 1) = 36n² - 1, which is equivalent to 35 (mod 36).

@trollme.trollmehard.9524 2 года назад

You know...I think I need to learn how to write proofs and videos like this are going to help get me there. Thanks.

@niamhgirling6000 2 года назад

Is there anything interesting about the amount of steps involved in the summing to arrive at the digital root?

@MrSpeedyAce 2 года назад

Loving the Klein Bottle on the shelf behind him. I have one too 😁🤙🏻

@philippepermanne1629 2 года назад

And if they are separated by 4, the sum will always be 5 ! :-)

@thegenxgamerguy6562 Год назад

Wow, I would really like to say "thank you" for this extraordinary prime number video. Why? Because I like to see proofs for very non-obvious things, and here we get TWO proofs for a very non-obvious thing, which is actually really exciting.

@PopeLando 2 года назад

I did 59 and 61, the product of which has a digit sum of 26. Then I found 4 digit twin primes and their 4 million + product... also had a digit sum of 26. ! PS I've just in the last couple of weeks been experimenting with the Goldbach Twin primes conjecture (every even number larger than 4208 is the sum of two twin primes - that's primes that happen to be twins, not twin prime pairs themselves), and I found out a lot of things about twin primes, but I never suspected that every digit root of their product would be 8. I'm now going to watch the remaining 13 minutes of this video and find out that I'm being an idiot. Edited: 9:15 Yay! This was the first proof I ever did on my own (and in base k digital root of any number n is n mod k-1)

@tobiaswilhelmi4819 2 года назад

"find out that I'm being an idiot." For the rescue of your honour: there are some mistakes that you can only perform with a certain level of expertise.

@chrisd561 2 года назад

Another banger video, Brad !!!

@RudyHHOfficial Год назад

There's another infinite sequence of twining: Step 1: Take a prime pair. Step 2: Multiply those. Step 3: Subtract that until you reach a twin prime. for (3, 5), I did: _(3, 5)_ (11, _13_ ) (137, _139_ ) and ( _18_ , _919_ , 19,079)

@BigTallLankyDude 2 года назад

4:53 "The prime numbers as you know start with 2..." *Matt Parker feels a disturbance in the force*

@antoniusnies-komponistpian2172 5 месяцев назад

The product is not only always (except 3*5) 8 mod9, but also 35 mod36

@SolinoOruki 2 года назад

He's the best math teacher I've ever seen

@jasonroberts2010 2 года назад

i find a clock to be a great intro to modular arithmetic. Everyone knows 11 + 2 = 1. Granted, there's no zero, but I find it an intuitive place to start.

@soberhippie 2 года назад

It would've been nice if Ben had a twin and they did the twin proofs for -seven brothers- twin primes

@RJSRdg 2 года назад

He does have a twin, but yes, it would have been nice if they'd done one proof each!

@SparksMaths Год назад

I'll ask my bro next time. :)

@HunterJE 10 месяцев назад

While I don't question the results I do like to think about the potential for stagecraft trickiness - the "well I already wrote my prediction so it doesn't matter if I see see the calculations" thing *could* potentially be used to trick a mark in to making any prediction work, at least for a single game, since once you're watching the calculation could just give arbitrary operations on the fly until an opportunity arose to give one that reaches whatever "prediction" you wrote down...

@s4623 2 года назад

Digital root for base n is equivalent to mod (n-1). Should be simple to generalize it.

@modernkennnern 2 года назад

`mod9 = digital root` is the only mathematical concept I've personally discovered

@JohnWFurst 2 года назад

Very well presented. Thank you.

@trequor 2 года назад

6:02 or as Matt Parker would say: "Two and three are the subprimes"

@douglasaziz4877 2 года назад

THIS WORKS FOR COUSIN PRIMES, Digital root is 5 for all cousin prime products. Cousin primes are always (n-2)(n+2) but n is divisible by 3. Therefore, (3k-2)(3k+2) =- 9K^2 -4 =5mod9

@2007screwball 2 года назад

I play with primes alot myself and have found something amazingly simple and answers many questions about the "randomness" of primes. If you'd like to see it, message me.

@KipIngram 4 месяца назад

I prefer that second proof, with (3*k+1)*(3*k-1). Very direct and clean and inarguable.

@Mr.Kent65 2 года назад

Thanks for giving mr a solution to my question

@JavSusLar 2 года назад

5:57 prime means first in Latin. Primes are always an exception toa rule because they are first... For example: every number ending in 5 is not prime except five itself.

@buildmaster6262 2 года назад

Twin primes? Exciting

@ygalel 2 года назад

Absolutely mind blown

@Abstract_zx 2 года назад

7:05 is it just a coincidence that these perfectly match up with the decimal digits of 1/7 (1, 4, 2, 8, 5, 7), but in a different order? or is there a reason for that behavior?

@brycephillips8738 2 года назад

Brady, long time viewer first time commenter here, love the channel👍( also from Adelaide) in a unrelated topic i think it would be really awesome if you could do a video about how to visulise very large numbers. i think it is(for me anyway) hard to understand how vast some of the numbers are, even a number 100 digits long is so massive. it would be awesome to have some visulisation on this. Thanks for the awesome content👍

@Shy--Tsunami 2 года назад

Would love to see Brady’s reaction when he’s involved in the questions. Would be awesome

@namduonghoang6301 2 года назад

@ffggddss Год назад

At 13 min, he replaces 9k² - 1 with 9k² + 8, which should instead be 9(k²-1) + 8. The argument from there, follows unaltered. Fred

@swirlingabyss 2 года назад

But won't this hold true for any two numbers on either side of a multiple of six, regardless of wether or not they are prime?

@supernovaaust 2 года назад

23 and 25 , both in the sequense of twin primes or 47 and 49, both containing a non prime do the same thing. 35 and 37 also., They are just the first 3 I checked. I image the same scenario leading to the conclusion that it is the sequence which produces these results and not the primes themselves...

@a0z9 2 года назад

La intuición a veces funciona. La demostración confirma la intuición. Prueba a poner esos productos en binario y obtendrás un patrón que te sorprenderá.

@mayankacharya2712 2 года назад

It's obvious that the multiplication for any two numbers [not necessary twin primes], (6m-1) and (6m+1); m belongs to N. Its digital root is always 8. i.e. The digital root of [36m^2-1] is always 8. OR mod9 of that is always 8.

@sexagesimalian 2 года назад

The 2nd proof shows that for any number n that is divisible by 3, the digital root of (n-1)*(n-+) is 8. None of of these numbers need to be prime. For example, n = 15 or n = 21.

@salvadorjacome2694 2 года назад

But that's the point. If that is true for ANY number, then is true for Twin Primes too.

@reinaldogarciagarcia9065 2 года назад

Particularizing the above for a pair of twin primes bigger than 3 (which always satisfy that they're separated by a multiple of 3), then you're done. It's is enough to prove a more general statement for any particular statement contained in it to hold true 🤷🏾‍♂️

@Bill_Woo 2 года назад

Does n-2 and n+2 do anything for you?

@JBLewis 2 года назад

@@salvadorjacome2694 THANK YOU! That's exactly what I was missing in the second proof. I felt like I was left hanging, and wasn't looping back around to the idea that ben was proving.

@GladionD.Pierce 2 месяца назад

Ben Sparks is a twin in his prime... :DDDDDDDDDDDDDDDDDD

@johng7410 2 года назад

Such a great teacher

@tw5718 2 года назад

The 2nd proof also says find any multiple of 3, the product of the number above and below have digital root 8, prime or not.

@MinorCirrus 2 года назад

Oddly enough, 1, 2, 4, 5, 7 and 8 are all the digits that repeat in the decimal writing of 1/2 (0.142857...). I cannot see how these are linked, but base 10 shure is poetic sometimes.

@ChrisContin Год назад

It’s not just “twin primes”- all primes are periodic, infinitely. Twin primes exist forever because 5 and 3 are prime. Start at 5 and move up by 2s. Another example are any two primes: 29 and 13 for example, 16 values apart. 29+16 isn’t prime, but 29+16+16 is 61 which is! Keeps going too.

@Edwin_Gan 2 года назад

I realized that the two proofs don't even need the fact that the twin primes are prime, just the fact that the twin numbers are not multiple of 3, so it will work for any 2 numbers of n-1 & n+1 (as long as both are not multiple of 3), like 35 (not a prime number) & 37.

@tentenbits 2 года назад

my favorite twin primes? Already covered that in my mega fav number video :) 8675309 and 8675311 are twin primes

@kenhaley4 2 года назад

This fact about twin primes actually has nothing to do with prime-ness per se. What's been proven here is that any two odd numbers separated by 2, with the number in between a multiple of 3 (e.g. 23 and 25 which are not twin primes), will have a product which has a digital root of 8. By the way, I love and look forward to every video featuring Ben Sparks. He truly makes math fun and enjoyable. Great to hear that he's a math teacher--I bet his students love him.

@Indian_Ravioli 2 года назад

The thing is .....any product of any 2 adjacent numbers either side of multiple of 3 like 25 and 23 would will have its digital root as 8. (23*25=575 whose digital toot is 8) Regardless of twin prime or not. In this case 25 is not prime.

@reluginbuhl 2 года назад

This was a fun one. The first proof did not seem to be quite complete to me though.

@brunoramey50 2 года назад

Not a mathematician, but, seems to me there's a bias there : this works with every pair of (n-1) (n+1) where n is multiple of 3. (n-1) and (n+1) may be primes or not. Example 44 x 46 = 2024. 2024 mod 9 = 8. To me, all of this as nothing to do with prime. Am I wrong ?

@goldenera7090 2 года назад

twin primes are always 6x + 1 and 6x -1 so 36x square - 1 will always have sum of digits = 8 qed

@rjrastapopoulos1595 2 года назад

Lol...I started with 3 and 5 and didn't get 8. Bad luck to stumble upon a counter-example right away.

@Misteribel 2 года назад

So any two numbers that are 2 apart, and the middle one is divisible by 3, will lead to a digital root of 8, right? Like 32 and 34. I mean it doesn’t just apply to twin primes per se.

@OBGynKenobi 2 года назад

If the digital root is adding the digits, is subtracting the digits called the digital tree?

@circuitgamer7759 2 года назад

I think I want to see if I can work out similar proofs for other bases... My guess is that not every base has an equivalent proof, but I can't say why yet. Should be fun!

@gurkiratsingh7tha993 2 года назад

James maynard is truly a legend

@sidimohamedbenelmalih7133 2 года назад

The same thing works on prime separated by 4 left 5 or 7

@WPGS25041941 7 месяцев назад

Can the Twin Prime Hypothesis be resolved within the axioms of arithmetic and elementary algebra ?

@amyparnell3325 2 года назад

When I first saw the title I was like “omg did someone finally solve the twin prime conjecture” but alas no, but still a great vid

@tomleroi636 2 года назад

What about the twin primes (difference 4 iso 2) 7 and 11, 13 and 17, 19 and 23, 37 and 41, 43 and 47, 67 and 71 (etc, same calculation method, always seems to end up in 5 or not?