I’ve always wondered: how feasible is it to implement an “isprime” function, via lookup table? If such methods are used, is cryptography getting weaker and weaker in practice as more large primes are discovered?
For smaller numbers see various prime sieves (Atkin, Eratosthenes)
Storage I have a harder time wrapping my head around. Aren’t primes quite sparse at cryptographic magnitudes? And are the primes used for (say) 256-bit encryption about the same magnitude, narrowing the dimension of storage required?
For RSA one typically use 2048 or 4096 bit primes.