- #1

KingGambit

- 37

- 27

- TL;DR Summary
- Public Key, Private Key, Prime Numbers, RSA, Encryption

Dear PF Forum,

Can someone help me with the algorithm for finding a very large prime number?

In RSA Encryption (1024 bit? 2048?, I forget, should look it up at wiki for that), Private Keys is a - two prime number packet.

Now, what I wonder is, what algorithm that the computer use to find those large prime number

Supposed one prime number is half of 1024, it's a 512 bit number, it's about 10^(512/10 *3) somewhere around 10^171.

And let's say we find some 10^171 number by random process, and if I were to check if it's prime or not, I would do a loop of 10 ^ 86, which is its square root.

Looping 10^86 is a very, very long time, and I see that Windows or Bitcoin node, give me a Private Key, relatively fast.

Even if we use array, which is very impossible, it would take computer with DDR 4 RAM as big as Milky Way I think.

I know, that I'm asking too much for an explanation here. But, I've tried to google the algorithm to find a very large number. I have found any luck so far.

So if someone perhaps know such link for that algorithm, I'd be really grateful.

Thank you.

Can someone help me with the algorithm for finding a very large prime number?

In RSA Encryption (1024 bit? 2048?, I forget, should look it up at wiki for that), Private Keys is a - two prime number packet.

Now, what I wonder is, what algorithm that the computer use to find those large prime number

**very fast?**Supposed one prime number is half of 1024, it's a 512 bit number, it's about 10^(512/10 *3) somewhere around 10^171.

And let's say we find some 10^171 number by random process, and if I were to check if it's prime or not, I would do a loop of 10 ^ 86, which is its square root.

Looping 10^86 is a very, very long time, and I see that Windows or Bitcoin node, give me a Private Key, relatively fast.

Even if we use array, which is very impossible, it would take computer with DDR 4 RAM as big as Milky Way I think.

I know, that I'm asking too much for an explanation here. But, I've tried to google the algorithm to find a very large number. I have found any luck so far.

So if someone perhaps know such link for that algorithm, I'd be really grateful.

Thank you.