I started a factorization project on numbers of the form 2x-c. The main goal is to arrive at new solutions to 2n = c (mod n).
I set up an ECM Server on superc.mooo.com 80 and welcome you to join in on the search with your computer's idle time. For a client, you basically just (1) download the software, (2) Edit the provided ecmclient.cfg file specifying your email address so I can properly credit you for any significant factors discovered , and finally (3) Run the client. It defaults to idle-mode so won't affect your computer's performance while you are using it.
For your convenience, I pre-configured and zip'd up all the essentials files for you here. Unzip these to a location on your hard drive, put your email address in ecmclient.cfg, and run ecmclient.exe.
Click here to download database of factorizations for c=3