we keep ours out - unrefrigerated and on the counter. We usually use them or give them away by week 2. We ate several this morning and they were delicious. We always use the oldest ones first.
If you wash them, you must refrigerate as you take off the bloom, or protective antibacterial coating. Once refrigerated, they must continue to stay in the fridge until use, but will stay good up to 6 months (or more) only who keeps eggs that long anyway. Oh, yeah, commercial egg producers. Store bought eggs can be an average of 3 weeks to 3 months old by the time you buy them. Fresh eggs are very hardy.
I was taught to always break eggs into a bowl, not the pan, in case of meat spots or any irregularities. I have never once found an egg that has gone bad, though, not even when I forgot a 1/2 dozen in the back of the fridge once and they were *really* old!
Eggs that are older than a week or so make great hard boiled eggs because they peel easily. Newly laid eggs are more difficult to peel when boiled as the internal shell membrane needs to dry a bit to separate from the shell. You have enough for a great egg salad or potatoe salad!
Best regards,
Kate