Prime Numbers are Computable. (Formula Given)

[Bobby_2021]

I lived my whole life thinking that prime numbers were unbreakable in the sense they can't be put into any equation.

But it can and mathematicians found out the formula even from 1960's.

Here is the formula. 

https://wikimedia.org/api/rest_v1/media/math/render/svg/350aec20a0065e791db5edf02d3731001cc43aac

Here is a neat explanation

Is there any problem in the world that is fundamentally uncomputable?

There are infinitely many primes and we can even find them using a formula.

What does this tell you about the nature of the universe?

What this tells is that complete comprehension of reality is indeed possible. Giving an equation for something is a sign of understanding what you were describing with that equation. An equation is an abstraction or understanding. So everything that can be defined or experienced can be understood. Incredible. 

[Scholar]

4 hours ago, Bobby_2021 said:

I lived my whole life thinking that prime numbers were unbreakable in the sense they can't be put into any equation.

But it can and mathematicians found out the formula even from 1960's.

Here is the formula. 

https://wikimedia.org/api/rest_v1/media/math/render/svg/350aec20a0065e791db5edf02d3731001cc43aac

Here is a neat explanation

Is there any problem in the world that is fundamentally uncomputable?

There are infinitely many primes and we can even find them using a formula.

What does this tell you about the nature of the universe?

What this tells is that complete comprehension of reality is indeed possible. Giving an equation for something is a sign of understanding what you were describing with that equation. An equation is an abstraction or understanding. So everything that can be defined or experienced can be understood. Incredible. 

Contemplate what understanding is.

[Leo Gura]

I don't think this is true. It would break encryption.

[zurew]

15 minutes ago, Leo Gura said:

I don't think this is true. It would break encryption.

Its true its just not efficiently computable. https://en.wikipedia.org/wiki/Formula_for_primes.

[Null Simplex]

Primes have always been computable.  The issue is they cannot be computed quickly.

[Yimpa]

11 hours ago, Bobby_2021 said:

What does this tell you about the nature of the universe?

Living a few miles away from an Amazon warehouse + Amazon Prime is heaven on earth.

[Bobby_2021]

10 hours ago, Leo Gura said:

I don't think this is true. It would break encryption.

It's only theoretically computable. Practically it's hard to get computing resources to compute multiple exponential functions and sum them over 2^n terms.

But it is indeed correct. Plug in the value of n and it spits out the nth prime number. 

The biggest prime as of now is (2^82589933)-1. We should just plug in this number as n and get the ((2^82589933)-1) th prime number. 

 

[Bobby_2021]

Prime numbers show how unique the creation is. No combination of previous numbers can make up the new prime number. It is completely new.

And there are infinitely many prime numbers as well. So the totally new creations that is possible is infinite and it is within the capacity of a mind to comprehend it.

l, ll, lll, llll, lllll, llllll, lllllll, .............

Prime numbers are a sign of emergence. Completely new stuff can show up from a system that cannot be found in any of its unique parts.  

 

[Leo Gura]

Fair enough.

[Meliodas]

but since it takes exponential time to figure it out , we can and probably break encryption with quantum computing , because we will compute in multiple states, thereby solving problems which take exponential time really fast

[Bobby_2021]

2 hours ago, Meliodas said:

but since it takes exponential time to figure it out , we can and probably break encryption with quantum computing , because we will compute in multiple states, thereby solving problems which take exponential time really fast

Soon. Waiting for a breakthrough. It will break the internet, literally.

[Carl-Richard]

The term you guys are looking for is "computationally intractable" 😉

[avatarse]

5 hours ago, Bobby_2021 said:

Soon. Waiting for a breakthrough. It will break the internet, literally.

FYI We have a few encryption alternative that does not use prime numbers.  I don't remember the details, but a competition was run semi-recently and they found a few alternatives. 

Realistically, this problem will either take so long to solve that we will have probably moved on already to another standard, or it continues to be a NP problem, in which case to break it in a realistic time frame will require quantum computing, and if we already have that we will probably be using a quantum computing based encryption method.

 

TLDR: Being able to compute primes easily would be a huge issue if someone suddenly discovered it, but the likelihood of that just happening(outside of an academic environment with actual experts) is basically 0%.  If someone did just figure it out, we'd deal with it and move on.