For example, there are about 2⁸⁰ primes less than 10²⁶, that is, with 26 or fewer digits. (Where could you get 2⁸⁰ bits of storage, even if you could do the huge computation necessary to check each of these?) 1024-bit primes are about 308 digits long.
You can imagine trying to get an intuition for a few different kinds of things:
* Up to what point has the primality of every number been checked?
* What is the largest general-form number whose primality has been checked conclusively? (or, what is the largest-known general-form prime?)
* What's the largest general-form semiprime that has been factored into primes without foreknowledge of the factors?
* How big are the primes we use in cryptography?
* How big are the largest-known (special-form) primes?
These things are very different orders of magnitude. I'm not sure of the exact answers to the first two, but I expect the first is below 20 digits (the π(n) calculations apparently didn't check all the individual numbers). The answers to the last 3 are: 232 digits, 308 to 1233 digits, and 22338618 digits.
https://en.wikipedia.org/wiki/List_of_prime_numbers#External...
But you couldn't hope to list all primes up to 1024 bits.
https://en.wikipedia.org/wiki/Prime-counting_function
https://en.wikipedia.org/wiki/Prime_number_theorem
For example, there are about 2⁸⁰ primes less than 10²⁶, that is, with 26 or fewer digits. (Where could you get 2⁸⁰ bits of storage, even if you could do the huge computation necessary to check each of these?) 1024-bit primes are about 308 digits long.
You can imagine trying to get an intuition for a few different kinds of things:
* Up to what point has the primality of every number been checked?
* What is the largest general-form number whose primality has been checked conclusively? (or, what is the largest-known general-form prime?)
* What's the largest general-form semiprime that has been factored into primes without foreknowledge of the factors?
* How big are the primes we use in cryptography?
* How big are the largest-known (special-form) primes?
These things are very different orders of magnitude. I'm not sure of the exact answers to the first two, but I expect the first is below 20 digits (the π(n) calculations apparently didn't check all the individual numbers). The answers to the last 3 are: 232 digits, 308 to 1233 digits, and 22338618 digits.