300 years. The time that various people in Final Empire thought it would take for the atium geodes to regrow in the pits after Kelsier brutalised them.
Possibly also not coincidentally the time between Hero of Ages and Alloy of Law. I rather suspect the atium cycle is back up and running.
Also people have the power of both Ruin and Preservation in them, could there be an esoteric way of "smelting" them down for atium or lerasium?