I have found (from experimentation so take it as you will) that fresh, free range eggs keep for about 3 weeks from the date of laying, if they are kept in a dark place that is reasonably cool, not necessarily in the fridge. If you are unsure about the egg you want to eat, and don't want to risk opening it to see if it's bad, then fill a cup/jug/bowl with water, make sure that the level of the water is at least twice as deep as the egg and then put the egg into the water...
If it floats, chuck it.
If it sits on it's end, eat it asap.
If it just sinks and sits there, it's still fresh
If you need cold(ish) storage - dig a hole and line with wet rocks - bottom, sides and top. Of course you have to make sure you put the food in a waterproof package. Once it dries out, wet it again. The evaporation will keep a steady temperature. It's obviously not a real fridge, but it will give you an extra day or two.
Hope that helps