I by no means am telling anyone what they should or should not crunch, but the more and more I have been looking into various projects the more I am wondering why some projects have such massive appeal. So I am a mathematician by training, so you would imagine I would be all over prime grid and a number of other mathematical based projects. In fact the state of things as they currently stand I crunch two "projects" World Community Grid, and GPU Grid. More on why to come later.
Sadly I feel the people that crunch any mathematical based project, really do it just for the cobblestones, and couldn't give a damn about what they are actually accomplishing. Finding a new prime number really won't change the world, and has just a minor impact on encryption schemes. Cracking a code ( Moo! Wrapper) by brute force is far worse than actually looking for prime numbers because in that case you are simply applying an algorithm to try and unscramble a message. Looking for a counter example to Collatz conjecture, or any other mathematical conjecture is not research. It is just letting your computer work through piles and piles of computation just for fun.
I am not sure there is a single mathematical conjecture on Boinc that has profound impact on the world, as they all tend to be in the purest of area's, in which showing that they are true might have some impact at some point in time, but guess what our computers could never show that these conjectures are true. We can check a google of numbers, do you know how many are left? (Infinite!) The longer these projects crunch the more we see that they could be true, but they can not be established as true until there is a proof that establishes them as fact. And before you bring the four color theorem into this which was "proved" by computers, that is far different than this. The difference is some mathematicians in that case developed an algorithm and classified all possible maps into a finite number of categories. They provided a proof that all maps had to fall into that finite number of categories, and then used the computers to check the coloring on each of those finite number of categories. As far as I have heard no such thing exists for any Mathematical Conjecture on Boinc, they are simply constantly checking a few more off the infinite list to check.
I would much rather see people contribute their crunching time to something that is doing actual research that can be conclusive in either way. If searching the stars are your thing then there are wonderful projects in which you can check for Extra Terrestrial life, or scan for pulsars. If you are a chemistry or physics enthusiast then there are wonderful projects working on research in each of those areas. If you want to feel like you are really contributing to the state of humanity by tackling medical, or world problems there are projects that can do that too. I fall in the later which is why I currently am focused on World Community Grid and GPU Grid.