A startup group could create an app where companies bid on user's processors. Users only can lose by not participating, so companies would have a huge pool of willing participants.
Facebook provides the accountability, allowing a trusted distributed computing community to form.
BTW, the RSA Factoring Challenge has been over for some time: http://www.rsa.com/rsalabs/node.asp?id=2092.
But back to my first point, what else - besides trying to factor big numbers - would I/you/a-20-something-hacker do with a big distributed network? I can't think of anything.