RSA key strength and math

TL;DR Since time is a factor here, $2048$ bit is probably fine for most systems and users as long as it is replaced often, like let's encrypt does with it's ninety-day lifetimes. However for an CA I wouldn't use less than $4096$ bit keys, and probably $8192$ bit keys if they where to live longer than ~2030 maybe. Update: There are algorithms with sub-exponential running time for factoring integers,