Depends how hot it is in your house, but they will easily keep a month in my house in summer on the bench. I don't refrigerate them at all. If they are getting old and you are concerned, put them in a jug of water and if they stay on the bottom, they are OK to eat. If they float, they are dodgy. I carefully crack those ones and if they smell OK I scramble them for the hens or cats or throw them out if they are bad.
I always cook older eggs thoroughly and keep the fresh ones to have fried or boiled with a soft yolk. There are also tips for keeping them by rubbing them in olive oil. In olden days they used to coat them in tallow wax. I would imagine dipping them in hot bees wax would also work....... being a beekeeper I have plenty of that. Must try it next time I'm melting some down!