As we’ve discussed before here, here, and here Timothy Gowers, Terence Tao, and many others have started using the Internet as a public forum for solving open reasearch questions in mathematics in which all good ideas are welcome. The general phrase for these projects is Polymath.
They have set up a webpage devoted the Polymath projects. In particular, they are already discussing a new problem which might be of interest:
Problem. Find a deterministic algorithm which, when given an integer k, is guaranteed to find a prime of at least k digits in length of time polynomial in k. You may assume as many standard conjectures in number theory (e.g. the generalised Riemann hypothesis) as necessary, but avoid powerful conjectures in complexity theory (e.g. P=BPP) if possible.
It’s a mixture of number theory (finding primes) and theoretical computer science (an algorithm which does it in polynomial time). If you’re interested in either, or just checking out what it looks like when math research happens, then head on over!