> Has there been "no progress" on classical prime factorization?

Not recently. The primality tests don't really help all that much. We already had polynomial tests that are really fast since the 70-s.

Think about this idea: the output of the counting function for the number of primes ("Euler's totient function") lies almost on the logarithmic curve, and we can compute logarithms quickly to any precision. So we can easily find the general area of the curve that should contain the current prime. And then we can quickly test if the given number is in fact the prime number within it.

This is probabilistic because the prime distribution is not _strictly_ logarithmic. We can imagine that by computing a logarithm we might end up in the next "bucket" and check for the wrong prime.

The fascinating part is that zeroes of the Riemann zeta function encode these corrections on top of the logarithmic curve. If the Riemann hypothesis is correct, then these corrections are _bounded_ and we simply can not end up in a different "bucket" by accident.