I don't wash mine unless they are visibly dirty, and only then just before using. The bloom that coats them when laid will seal in the moisture and the bacteria out. Unwashed, you can get at least a week out of them sitting on the counter, at a reasonable (not too hot) temperature (as if they were just hanging out in a clutch waiting to be sat on). In the fridge, pointy end down and unwashed, I've heard they'll stay fresh up to 6 months (although I've never tested that because I've never kept one that long). Washed, they'll keep like a store-bought egg, and start losing moisture and not be as firm after 3 weeks. Store bought eggs are washed and coated with mineral oil, which is not as effective as the au natural. It is my theory also, that you can wash germs in if you try to wash them off (shells are porous). That is why I don't wash the dirty ones until right before I use them, so that the bacteria would not have time to multiply within the egg. But if you cook them completely, you'll take care of the bacteria anyway, but my husband likes his over easy.
Also, keep them in a carton, which will prevent fridge odors from permeating your eggs and giving them an off flavor. And don't store them in the door of the fridge, but on the shelves instead because the door area will not keep as consistently cold as the interior.
Also, keep them in a carton, which will prevent fridge odors from permeating your eggs and giving them an off flavor. And don't store them in the door of the fridge, but on the shelves instead because the door area will not keep as consistently cold as the interior.