(Soft Question) Largest known semiprimes with no known factors

Question

Is there a list, similar to prime numbers and probable primes, of the largest semiprimes with unknown factors? Is there a list of numbers that are either semiprime or prime, with no known factors? Is there literature on how to find large semi primes?

Answer 1

It doesn't exist. Any area of rectangle which sides are prime is a semiprime.

Answer 2

As mentioned, this is apparently possible using some trick with elliptical something or other.

That said, it's also easy to build a poor man's version. Take some $n$; test it for primality; if it's not prime, test all prime factors up to $n^{1/3}$ to see if any divide $n$; if none do, then this is a semiprime with two large but totally unknown factors; otherwise, increment $n$ and repeat until you find one.