User blog comment:Deedlit11/Problems for the Second International Googological Olympiad/@comment-24923514-20170326183845/@comment-1605058-20170326185411

Deedlit has written up some of the solutions to these problems here, a solution to problem 2 is included there. The idea is to use a (rather difficult to prove) result from number theory which gives you very good and somewhat tight estimates on the n-th prime as a function of n.