cryptography - How many prime numbers are there (available for RSA encryption)? -

am mistaken in thinking security of rsa encryption, in general, limited amount of known prime numbers?

to crack (or create) private key, 1 has combine right pair of prime numbers.

is impossible publish list of prime numbers in range used rsa? or list sufficiently large make brute force attack unlikely? wouldn't there "commonly used" prime numbers?

rsa doesn't pick list of known primes: generates new large number, applies algorithm find nearby number prime. see this useful description of large prime generation):

the standard way generate big prime numbers take preselected random number of desired length, apply fermat test (best base 2 can optimized speed) , apply number of miller-rabin tests (depending on length , allowed error rate 2−100) number prime number.

(you might ask why, in case, we're not using approach when try , find larger , larger primes. answer largest known prime has on 17 million digits- far beyond large numbers typically used in cryptography).

as whether collisions possible- modern key sizes (depending on desired security) range 1024 4096, means prime numbers range 512 2048 bits. means prime numbers on order of 2^512: on 150 digits long.

we can estimate density of primes using 1 / ln(n) (see here). means among these 10^150 numbers, there approximately 10^150/ln(10^150) primes, works out 2.8x10^147 primes choose from- more fit list!!

so yes- number of primes in range staggeringly enormous, , collisions impossible. (even if generated trillion possible prime numbers, forming septillion combinations, chance of 2 of them being same prime number 10^-123).