# Number theory research topics

I have to do a project for my number theory class (Undergraduate). The professor asked us to explore a topic from number theory and write about 5 to 10 pages on it.

I am a computer science major, so I really want a topic that relates to computing too.

I am personally interested in the twin prime conjecture and prime divisibility tests and algorithms

The prof said that the ABC conjecture is also a good one.

Can any body suggest other good topics ?

And your opinions whether it is good or not to make a project on the twin prime conjecture or prime divisibility

You may want to consider Collatz conjecture (aka the $3n+1$ conjecture).
Something like elliptic curves, which are smooth projective cubic curves. Roughly speaking you can put a group law on points of the curve, by a simple geometric method, and this group structure is also used in cryptography : as well as you can use $\mathbf{Z}/n\mathbf{Z}$'s groups, you could used other groups, as those of elliptic curves.