I'm pretty sure that the sum of previous primes plus 1 is always a prime number. But idk

So 2x3x5 + 1 = 31 type of stuff

Actually I just figured out that my assumption was probably wrong

i don't know why i pretended to be retarded. i have shamed myself. i'm sorry..

30031 is not prime and it is the first number that this does not hold

It's ok

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59 × 509 = 2x3x5x7x11x13 + 1
I tried using the logic for proving the existence of infinite primes but realized that it doesn't work

Did you see Euclid's proof on infinite primes

Yes, I have seen it. I was inspired by that but realized that the reason it works is because it implicitly assumes that there are no more primes between the product and the prime of the highest value, which is not true when you try to make it finite .

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Exactly. Also maybe you don't realize if you'd find an "easy" formula like this for constructing primes then you would have turned the entire math and compsci world on its head. All of our encryption would fall apart, just like if it would with P = NP

Asus Z390 PRIME x 9900K + 1 Titan RTX = Housefire(Not prime)

7 * 5 + 1 = 36 which is composite

I said all primes before it yo not just some

So it wouldn't be an easy formula because it wouldn't give you all primes. It would only give you some of them and you would have to calculate all the primes in between. Also I'm not sure if we have proven that finding primes is an np problem . As far as I know it is undecided but I could be wrong.

Also RSA encryption is about factoring primes and not constructing them. So it wouldn't break RSA

Eh I'm a bit hazy myself. I'm sure one specific version of factorization is in NP but I can't remember which one, but in any case they're all pretty closely connected
If you can find a way to easily construct them then you automatically have a way to easily factor them. Worst case scenario you start with the largest prime lower than the square root of the number you're factoring and run down your list of primes from there. Even with a shitty algorithm like this it's still gonna be leagues better than present day standards simply because the list of primes is a given

I know that factorization is NP but i'm not sure if discovery is. I know that checking if something is prime isn't NP (It is P) even though it was expected to be
>If you can find a way to easily construct them then you automatically have a way to easily factor them
can you try and explain why or link me to something that can?.