Just a quick query: Who has done any work with the Busy Beaver problem? Me and a small group of kids in my Discrete Math class have taken on trying to prove BB5. We have met with moderate success, currently with only 1 billion machines to process. I have drained the every online resource I could find, including all work on the subject posted to newsgroups since 1989. I have read the papers done by Heiner Marxen, and anything that comes up in a Google Search for 30 some pages. If anyone has some useful resources, please share.