It depends if they are covered in poop and bacteria - this will potentially make them go off quicker if the bacteria gets into the eggs. We crack all our older eggs (up to about 4 weeks old) onto a saucer, one at a time before using or cooking. If they go splat and the yolk disintegrates and the white collapses flat we throw it out or feed it to the dog. If it looks fairly OK and intact we use it. We haven't died of salmonella poisoning (yet).
Recently it occurred to me (even though I knew this) that you can easily freeze eggs for later use and they will keep for up to 12 months frozen. There are several ways to do this: you can just put them in a freezer bag or container still in shell (the shells may crack though), you can crack them open and put them into ice-cube trays then empty trays into freezer bags once frozen, or you can roughly beat them (scramble them) and freeze a quantity of them like this in any container. If you Google about freezing eggs you can find plenty of ideas on it.
Contrary to popular belief I do wash my eggs however. The egg producers HAVE to wash and sanitise their eggs and the big hatcheries do it as well. Wash eggs in warm to hot water with antibacterial dishwashing liquid, rinse in warm to hot water then dunk in a sodium hypochlorite bleach solution (50 ml of 1% w/w concentrate (Miltons) to 2 litres of water) that is warm to hot, dunk only briefly to fully cover, and allow to air dry on a towel. I don't have the desired dilution ratio on hand, just know I worked it out once and it works at that ratio with the Miltons 1%. I think it equates to dilution of 0.25 parts bleach (25 ml at 1% bleach) in 1000 of water (1 litre). BUT you can get stronger sodium hypochlorite bleach much cheaper at Bunnings or the supermarket than Miltons so don't waste your money. Adjust dilution accordingly though, so if you buy a 6% w/w active constituent at Bunnings then you just need a touch over 4 ml per litre of water etc.
Washing eggs will mitigate the likelihood of bacterial contamination dramatically but will probably shorten the shelf life of eggs a little because it removes the protective bloom and makes the shell more porous (which probably just means the egg contents dehydrate quicker and therefore become "staler" quicker). I give washed eggs 4 weeks till use by date from the date laid if refrigerated. If not refrigerated straight away and the weather is warm to hot I may shorten this to about 3 weeks. For me, the proof of freshness is when I crack them into the saucer. I do write the date laid on all eggs with a soft pencil (2B pencil).
Some people are vehemently opposed to washing any eggs, but quite frankly, I don't want loose dirt and poop falling into my cooking when I crack an egg, that's disgusting, and is probably the greatest point when bacteria is transferred into the human food chain (think about how the egg contacts parts of the cracked shell when you crack it into your cooking

). You see, despite all the old beliefs, people just don't think it through rationally. I also wash and sanitise incubating eggs the same way, with just as good if not better hatching results.

(Truly - I know it's hard to fathom!

)