Prime Number Perfection #shorts

Usually when you look at a nice round or coordinated number, it's components are obvious. Like 333 -- you know there are 111 threes in there, and even 111 is made up of 37 threes. 1,000 is 10 hundreds, and those hundreds are 10 10's. But when you break down 1,111,111, you find that it stems from a combination of two prime numbers that are pretty much random. How can something so perfectly symmetrical come from such weird pieces? Well, IT DOES.

You know #shorts

[Mikeastro]

There are many more numbers with only 1's that are composed of precisely two prime factors:
111 = 3*37
1111 = 11*101 (though this one is kinda obvious)
= 41*271
= 239*4649
= 21649*513239
I expect there to be even more impressive examples but I'm too lazy to search farther right now

[McPilch]

Imagine being Kevin's partner or housemate. How often would you get randomly interrupted by Kevin excitedly coming up to you with a whiteboard and a wild look in his eyes, exclaiming "CHECK THIS OUT!"

"Yes, Kevin, very cool, now can you please close the bathroom door, I'm kind of busy..."

[screenzombie]

I like that after this, you can show that 1, 111, 111 squared is 1, 234, 567, 654, 321 which is also a really cool palindromic number.

[MrPerfs]

I think the most impressive "oops all ones" belongs to the largest known prime number, when written in binary it is a continuous string of 82, 589, 933 ones

[TheOrigamiGenius]

1 may seem small, but it's connected to every prime number

[snwO]

"No relation..."
Me:
"but when you multiply them together-"
Me: there it is...

[grainfrizz]

Well, we only think 1, 111, 111 is special because we're reading base10. But in other bases, it's nothing close to cute.

[mx_nana_banana]

I have a name for numbers like this, military numbers, because all the ones look like mini soldiers.

[diamondcreepah]

"these two numbers have no connection to eachother whatsoever"
Continues to explain how they're connected

[UpdateFreak]

"They have no relation to each other"
The 9 they both have in their last digit: Am I a joke to you?

[guyvisual]

356 and 195 are also normal-looking numbers, but if you multiply them, you get something beautiful :)

[raid.leader]

I'm farming a perfect Palindrome this week

[Noname-]

Numbers can behave in many unexpected way. Not really related but one of the direct consequence of Euler's theorem (number theory) is that:

Any integer n that is relatively prime to 10 is a divisor of 99...99 with some amount of digits m (there are infinite solution of m for each n because modulo arithmetic respect exponentiation), one of the solution being m equal to the Euler's totient function of n (which is the amount of number between 0 and n that are relatively prime to n).

For example, n=21, there are 12 numbers between 0 and 21 which 21 is relatively prime to 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20 so is a multiple of 21. Since you can find 99...99 that is divisible by any 9n, you can find 11...11 that is divisible by any n.

[oldmemesrgud]

Imagine being a computer scientist and mixing that number up with its binary counterpart

[FewVidsJustComments]

That cereal reference at the end killed me xD

[brianviktor]

"The only factors of 1.111.111 is 1 and itself." -> Well, and 4649 and 239 obviously...

[dataandcolours]

Just some additional info. Following from Euler's theorem this entails that the cycle length of the decimal pattern for 1/239 and 1/4649 will both be 7 since there are seven "ones" in
In fact your previous video where you talked about 1/7 and the 0.142857 is connected to that 7 divides

[Rabbit-the-One]

Well done. I'm happy to have gained this information.

[_rd_]

This video presented it in reverse, giving the illusion that it's an unseen miracle, but looking from checking the symmetric number perspective it's pretty easy to find.

You don't multiply random prime numbers until you find a symmetrical result. You check symmetrical numbers until you find one with only prime factors, which is easy

[vampire_catgirl]

I don't think there's a single 'all ones' number that doesn't have prime factorization