Would it be possible to patent Bitcoin? Bitcoin utilizes a proof-of-work mechanism to assure against double-spending, as well as providing an example opensource implementation.  However, some countries allow software patents, which could mean that one person/company has the ability to suddenly prevent the legal use of Satoshi Nakamoto's Bitcoin algorithms.

Are these Bitcoin algorithms complex enough to qualify for being patentable, and if so, in what countries might such patents be granted?  Does this pose a significant legal risk for users of Bitcoin?
To claim a patent you must be able to prove against contest that you invented the device, and have a working example that if built to the specs provided, runs. 

As it was this Satoshi who invented bitcoin, and there are prior examples of a digital currency, it would be very hard for any one person to claim a patent so far after the fact. Some one could try, but the patent industry is built to make it hard to write a patent, easy to contest. Admitedly many companies do just that and are good at it, but anyone patenting bitcoin would have a hell of a time proving first invent.