PokeVideoPlayer v23.9-app.js-020924_
0143ab93_videojs8_1563605_YT_2d24ba15 licensed under gpl3-or-later
ImmersiveAmbientModecolor: #c3b197 (color 2)
Video Format : (720p) openh264 ( https://github.com/cisco/openh264) mp4a.40.2 | 44100Hz
Audio Format: 140 ( High )
PokeEncryptID: ddab56a271c6d6cbda94c5bb67074727ffed656f2d5f0c0b9d93c080ae9d69bc0b1971ea6c605581762d71c88725d9e0
Proxy : eu-proxy.poketube.fun - refresh the page to change the proxy location
Date : 1738867352550 - unknown on Apple WebKit
Mystery text : SThsQW9iT2lkdm8gaSAgbG92ICB1IGV1LXByb3h5LnBva2V0dWJlLmZ1bg==
143 : true
67,476 Views • Dec 28, 2023 • Click to toggle off description
Views : 67,476
Genre: People & Blogs
License: Standard YouTube License
Uploaded At Dec 28, 2023 ^^
warning: returnyoutubedislikes may not be accurate, this is just an estiment ehe :3
Rating : 4.935 (62/3,778 LTDR)
98.39% of the users lieked the video!!
1.61% of the users dislieked the video!!
User score: 97.58- Overwhelmingly Positive
RYD date created : 2025-02-06T18:13:59.638697Z
See in json
133 Comments
Top Comments of this video!! :3
Do the opposite. Start with 8, show it can lead to an infinite amount of twin primes and bingo you solved the conjecture. Very easy. Maybe one day I will share my proof.
330 |
You definitely should do more. Just try the same approach with base-37, and now you will always end up with a digit, that represents 35. How cool it is!
3 |
These comes from 2 well-known facts from number theory.
1. Every prime >3 is 1 apart from a multiple of 6.
2. In base 10 the sum of the digits has the same remainder modulo 9 as the number itself.
Applying (1) we get the the two primes are necessarily (6k-1) and (6k+1), so their product is (6k-1)•(6k+1) = 36•k^2-1.
Now lets apply (2) and reduce it modulo 9.
36•k^2 - 1 = 9(4k^2) - 1 = -1 = 8 (mod 9)
Here you go.
116 |
When you have a pair (a, b) that is 2 apart (in other words, b = a+2) and both are greater than 3 , then either
- one of (a,b) is a positive multiple of 3 (but not 3 itself) and hence is not prime; or
- the pair (a,b) is congruent to one of the three following cases:
(a,b) = (2, 4) mod 9 OR
(a,b) = (5, 7) mod 9 = (-4, -2) mod 9 OR
(a,b) = (8, 1) mod 9 ,
and hence their product a*b = 8 mod 9 .
In other words, the property also applies to "twins" that aren't both primes and of which neither is a multiple of 3 ; for example:
8 * 10 = 80 ==> sum of digits: 8+0 = 8
23 * 25 = 575 ==> sum of digits: 5+7+5 = 17 , 1+7 = 8
119 *121 = 14399 ==> sum of digits: 1+4+3+9+9 = 26 , 2+6 = 8
|
But isnt this true for any pair of numbers above and below a multiple of six? I don’t see why this is special to prime numbers only? Take for instance 23 and 25. Then 23x25 =575 -> 17 -> 8 but 25 is definitely not prime.
40 |
Because all those products are one less than a multiple of 36, so in particular they are 8 when taken modulo 9... Hence the sum of digits property
8 |
I thought of a possible way to solve it but I am not good at proofs so I don’t know how I could apply my idea
30 |
I have also noticed that the product of two twin primes is always one less than a perfect square, which is proved as follows:
the product of 2 twin primes
p(p+2)
where p+2 is also prime is p² + 2p, which is one less than p² + 2p + 1, or (p+1)², so p(p+2) = (p+1)² -1,
or, the product of 2 twin primes is always 1 less than a perfect square.
1 |
Here's a possibly dumb thought. Every pair of numbers satisfying (6p-1, 6p+1) where p is a prime number or 1, is a twin prime. If this is true, then the twin prime conjecture is true as well since there's an infinite number of prime numbers.
|
Math is elegant
|
That’s cool. Why except for 3 and 5?
16 |
Wow, awesome 😎❤
1 |
I see (X-k)(X+k)=(X^2)-k^2. For this case x is sandwiched between primes and k is 1.
5 |
Do it in other bases, i expect binary to be interesting
6 |
Adding the numbers together is the same as doing mod 9
|
I actually saw a pattern predictable pattern to do with twin primes when i was playing around
But like... i don't want to do anything with it
|
This is true of any two +- 1 a multiple of 6 multiplied together. so is not a property of twin primes.
|
Try it in base 3.
12 x 21 = 1022
102 x 111 = 12022
122 x 201 = 102222
4 |
It might be impossible to prove or disprove the twin prime theory.
|
@isaiahgreenlee9273
6 months ago
For the curious:
This happens because in base 10, adding the digits together repeatedly in this way reduces a number modulo 9 (gives the remainder when divided by 9)
Now, call the primes n+1 and n-1, where n is the number between them. Multiplying them together yields:
(n+1)(n-1) = n^2 - 1
For any three numbers n-1, n, and n+1, one of the three must be divisible by 3, and since n+1 and n-1 are prime, n must be the multiple of 3 (unless one of the twin primes is 3, in which case this property doesn't hold), which means n^2 is a multiple of 9. So subtracting 1 from n^2 always gives a result that is 1 less than a multiple of 9, or 8 more than a multiple of nine. This is where the 8 comes from when reducing mod 9 by repeatedly adding digits.
1.3K |