I've eaten 8 day old eggs from the coop before, in mild weather, say, 75 to 85 degree weather here in Texas, the yolks were runnier then usual and they did have a stronger egg flavor, and 5 day old eggs out of the coop in 90 plus weather that were still fine.
I just crack them in a bowl separately before I add them to the pan or whatever if I question them.
At room temp they are good for 2 -3 weeks, but I do throw out any egg with the slightest crack in them, well, I cook them for the chooks or the dog if they are only a day or two old. At the very least, don't waste them completely, you can keep the shells to add back into your chicken feed or compost, if your worried about rotten egg, then bake the rinsed shells a bit, that is very valuable calcium to your chicks, and our heritage and home grown breeds have way thicker shells then that of the store bought variety, and therefore use up more calcium.
Extra calcium in your compost keeps your tomatoes skins from splitting as they grow, btw.
