[test77777]

I’d argue that you’re just misunderstanding what makes a number prime. You can literally never be 100% sure a randomly generated number is or isn’t prime, it’s just the way numbers work.

[magneticnorth]

I think you have some confusion about RSA cryptography - it relies on numbers that are deliberately generated using very large (known) primes, so these numbers are definitely not "randomly generated".

It takes a short time to generate such a number but a very long time to decompose it, but this is a different problem than telling whether a number is prime.

[vlovich123]

The primes used in RSA are definitely randomly generated for each new key, unless I’m misunderstanding what you’re trying to say. And afaik determining that the random number is prime is a mixture of “generate a random number using a formula that has a high probability of generating primes” and various probabilistic primality tests. It’s possible AKS has been incorporated to prove the numbers are prime in modern implementations, not sure. But historically RSA traditionally (definitely before 2006) determined primality probabilistically.

ECC doesn’t require primes and so is safer in that respect although I’ve been hearing that ECC might have structural deficiencies that causes a swing back to RSA for the most secure applications.

[JonChesterfield]

Counterexample, roll a dice. That gives you a randomly generated number. You can then test whether said random number is prime by enumeration.

[Ar-Curunir]

There is literally an entirely deterministic algorithm for checking primality, so you can be 100% sure that a randomly-generated number is prime: https://en.wikipedia.org/wiki/AKS_primality_test

[adgjlsfhk1]

you absolutely can. aks is a polynomial time deterministic primality check.

[test77777]

Ok then break all cryptography with that. It just proves my point you can SAY you can do it but in practice you can’t.