Can I put hard boiled eggs in a compost or a worm bin?

Hi, I have about a dozen hard boiled eggs left over and I was wondering if I can put them in my compost bin or my worm bin. I've always read you can add the egg shells but never on weather the contents of the eggs shells can go in and why not if they can't. Anyway, if I have a preference it would be to give them to the worms as we've been light in feeding them this week. Thanks!