Closely related: what is the smallest known composite which has not been factored? If these numbers cannot be specified, knowing their approximate size would be interesting. E.g. can current methods factor an arbitrary 200 digit number in a few hours (days? months? or what?). Can current methods certify that an arbitrary 1000 digit number is prime, or composite in a few hours (days? months? not at all?).
Any broad-brush comments on the current status of primality proving, and how active this field is would be appreciated as well. Same for factoring.
Edit: perhaps my header question was something of a troll. I am not interested in lists. But if anyone could shed light on the answers to the portion of my question starting with "E.g.". it would be appreciated. (I could answer it in 1990, but what is the status today?)
