Primes with Primitive Roots near powers of two

For every power of two, what is the largest prime number less than it for which a primitive root is known? This probably means what's the largest prime number p less than 2^n for which p-1 has been completely factored. I guess it also begs the question, for each Mersenne prime 2^p-1, is 2^p-2 factored? Another related question is what's the largest Sophie Germain prime less than 2^n, for each prime (because sophie germain primes minus easily factor). Of course, there's also: what's the smallest prime number greater than the power of two that yadda yadda...