Rainbow tables allow you to choose a tradeoff between storage and speed. So if you wanted to do that (which is of course unrelated to Bitcoin), the actual constraint is: (table size) * (number of hash calls to invert one hash value) = 2^256.
So, if you magically transformed the Earth into a giant rainbow table that uses N atoms to store a key value pair, you would have to perform N*10^27 hash calls to invert one hash value. Not very useful in this case.
Now you can donate to Singularity Institute using Bitcoin.
Currently Bitcoin mining appears to be profitable as only bubble economics can be. Already some Less Wrong users have purchased GPUs and started mining Bitcoin. Please consider sending some Bitcoins to SI at address 1HUrNJfVFwQkbuMXwiPxSQcpyr3ktn1wc9
2014 Edit: Please donate Bitcoin by using the Bitpay link on MIRI's donate page. Thanks!