In the context of a new largest (mersenne) prime number being found this week -
The largest known prime number is now
2^57,885,161 − 1, and it took 5 years to find it since the last largest prime was found.
But we know that various asymmetric encryption algorithms require ridiculously large primes which are used as the infamous
q factors. For example, 1024-bit RSA would require two 512-bit primes.
But this article, if correct, claims we are able to enumerate no more than
~1.7M prime numbers.
How does this settle with cryptographic prime number generation?