Answer: 3
Of course, as time passes, the smallest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration.

Answer: Yes, it is!
Adding up the divisors of 8128: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064 = 8128