How do I choose an appropriate scope for a master's thesis in mathematics? I am a new Master's seeking student in Mathematics, and I'm trying to get a jump on my research focus/concentration for eventually writing my Master's Thesis. My interest is primarily prime, perfect, and Mersenne numbers. When I try to formulate a plan though, my ideas are always too broad and vague, or are way too specific. Does anybody have advice on how to decide on a topic? How long is the average such thesis? Perhaps what I thought was too vague and expansive would be a perfect length and I was just second-guessing myself too much.
To expand on scaaahu's very valid comment, consider the following:


what specific topic(s) interest you the most.
which of these do you have some level of confidence in pursuing at a Master's level.
Who has the expertise to be able to advise you, are the willing to do so (they may be overloaded).
Are their enough resources available to start research in the chosen field.
Finally, what is the 'end-game', where do you hope to go with this qualification?