When a hen lays an egg, she puts a coating on it called bloom, that helps keep bacteria out. It is not a perfect barrier, but it really helps. If you take that bloom off, they really need to be refrigerated. They can last months in the refrigerator. So if you wash them, you need to refrigerate them.
If you do not wash that bloom off and they are not very dirty, you can store them on your counter for several weeks if your kitchen temperature is not too warm. The warmer the room is, the faster they may spoil. If you are in the low 70's, I would not worry about keeping them 3 weeks and they will probably last a lot longer. But if bacteria ever gets inside, it can multiplky pretty fast if the egg is warm.
Another possible issue is with fertile eggs. They are not going to hatch on your counter, but if the temperature gets too warm, they may start to develop a little. They don't have to be at true incubation temperature. the lower 80's is warm enough to get some development. That does not mean they are not safe to eat. They don't necessarily have bacteria in them if they start to develp, but I personally would not want to eat that egg.
If an egg is dirty, that dirt can have bacteria in it. I wash my dirty eggs and store them in my refrigerator. It is recommended that you use water at least 10 degreees F warmer than the egg if you wash it. The reason is that if the air sac cools off, it can contract, create a suction on the egg shell, and suck water into the egg. That water might carry bacteria in with it. If you use warm water, that sir sac expands, created a little pressure in the egg, and keeps that water out. By the time it cools off , it is either dry or you have finished washing it and only clean water is available to be sucked in when it cools off again. That is probably overthinking it, but why not be safe?
I store my clean eggs on the kitchen counter, sometimes for three or four weeks. In any case, I always break an egg in a separate bowl before I mix it with anything just in case, but I have not found anything developing in there that could cause a concern. But some day I may, and occasionally I find blood spots or meat spots. I think breaking it in a bowlk is just good practice.
So store them wherever you want, but they will probably last longer in the refrigerator.