That is a good question.  Are you talking about fresh farm eggs or store boughten?  The ones from the store the recommendation is 2-5 weeks but that doesn't mean they are always spoiled.  The ones gathered fresh from the farm will probably last longer since they are usually fresher to start with.  

The key is to keep them in closed cartons and refrigerated, so they don't dry out.  The eggshells are permeable so exposed to air for long periods of time the egg contents 
will dry out and lose quality.  

It is pretty easy to tell if an egg is ok to use by cracking it out of the shell.  If it looks like an egg and the yolk is still in tack and smells ok, go ahead and cook it well and use it.  If it is really watery and the yolk is watery you probably don't want to eat it. It will probably also have an off odor when cracked.  

Always cook your egg before eating for safety. The bacteria that can make you sick found in eggs is destroyed by cooking the raw egg and then refrigerating with in 2 hours.  

As for hard cook eggs.  If they were properly refrigerated within a couple hours of cooking, they can last up to two weeks in the shell.  

Hope that help.

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Nellie Oehler