Create a computer that will calculate digits of pi continuously, probably using a spigot algorithm, and store them. The point is a technology demonstration of a computer system designed to run forever reliably (very different from the mentality of a box that you throw away every few years).
Automatically do checkpointing. If any component fails or needs to be upgraded, or we run out of memory or disk space, the program gracefully shuts down and can be restarted. Any hardware error will eventually be detected and corrected by means of redundant computations and storage. This probably means periodically rerunning the computation from scratch on a higher priority thread than the main thread (so it can catch up). Stored digits are periodically tested against checksums.
The general idea is, dealing with all manner of things that can go "wrong", interrupting the smooth flow of computation, are already designed into the routine maintenance plan of the system.
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