Number theory is an enormous field of research. You can get a good impression of the types of topics I am interested in by
There are links between the research I do in number theory and techniques from algebraic geometry, representation theory, symbolic and numerical computation. I tend to suggest projects on topics that are closely related to my research interests; in my experience this works well for both my students and myself. I am not opposed to supervising a project on a topic that you choose yourself, but be prepared to work more independently in this case.