If you have eggs in the refrigerator that have been there for days or maybe even weeks, there is always a question of freshness and safety of the egg. If I absolutely have to buy factory eggs during the winter when fresh farm eggs are not available, I often keep them far too long because I really don't like the taste.
The easy test for eggs is to fill a deep bowl full of water, and place an egg in it. The air pocket on fresh eggs is about the size of a dime, and thin. Very fresh eggs will sink to the bottom and lie on their side; eggs a week or so old will lie on the bottom too, but bob slightly. As the eggs get older, the air pocket inside the shell increases; a 3 week old egg will float with the narrow end pointed down, and a bad egg will just float and/or bob around. A fresh egg cracked onto a flat plate will have a yolk that stands firm and high, with a white that is thick and close to the yolk. As eggs age, the yolk and egg white both lose elasticity; the yolk becomes flatter, and the white runny.
Why do they float? Partly due to the 'cleanliness' fetish.
All eggs (chicken, duck, goose... ostrich) are laid with a mucilaginous coating on the outside of the shell, which acts as a protective barrier. It is designed to keep air (and thus bacteria) out of the egg while the embryo grows into a chick. All factory eggs are washed of this protective coating, leaving the shells porous. Porous eggs do not keep well or long, even refrigerated, as they allow air penetration and ultimately spoilage. Also, most refrigerator air will hold odors of stored (or overlooked, spoiled) foods and can transfer those odors to the already porous eggs.
My mother kept eggs, unwashed (unless exceptionally dirty) in an egg cupboard on the wall in the cool pantry. Most eggs were used within a week or so of being laid, only washed just before cracking, and with a date penciled on each egg so the oldest were used first. My grandmother kept eggs in the cool cellar for months by coating them with paraffin or vaseline and storing in a bowl, or immersed in a crock of lard, but the eggs had to be fresh and unwashed, and preferably non-fertile.
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The reason for using non-fertile eggs has to do with incubation temps of fertile eggs. Fertile eggs are usually in a nest (before the hen actually sets them) for only a day or so at normal outdoor temperatures. However, if the proper incubating temperature of about 102.5ºF is not reached soon and maintained, the fertile embryo will die and cause the egg to decay.
You can use fertile eggs for storage but you must be sure they are fresh that day. One bad egg in a crock of lard is just as bad as one bad apple in a bushel... both will spoil the others around them.
Almost all of the fresh, free-range eggs I find lately at the farmer's markets have been washed. So while they look clean and pretty, they don't keep well, and I have to refrigerate them even though I use them within a week or so. I'm working on a couple of farmers to keep some unwashed eggs aside for me until I have my own layers. They usually forget, probably because one of the children collects and washes the eggs... and not always the same child.
Once I have my own eggs, I will experiment with different long-term storage methods including coating with beeswax, immersing in waterglass (sodium silicate), lard or olive oil in a crock; coated eggs covered in bran or sawdust mixed with salt, and perhaps other methods as I find them. I doubt I will try vaseline or any other petroleum-based material except probably paraffin, just on general principles (same for GMO oils).
I really would like to be able to store local free-range eggs over the winter in my root cellar so I always have good eggs available even when the local hens aren't laying.