Weeks, potentially months.

When I was a kid we’d get farm fresh eggs and store them in a non-self defrosting refrigerator 6 months and they were still good.

Today, eggs keep best if they’re in a Styrofoam carton, or otherwise protected from the self defrosting mechanism of the refrigerator. The egg shells are porous, and, quite simply, the fridge with dehydrate them over time.

If you’re in doubt, you can fill a bowl with cold water. Gently submerge your egg in the water. If it stays on the bottom, it’s good to eat.
If it rises a bit of rises to the top, you can either discard the egg, or crack them individually into a cup. If they smell and look okay, and you’re not eating them raw, they should be fine. A rotten egg is very apparent.

Short answer: Yes. Your eggs will keep 4 days.

I keep them for months. Four, five months easily.

Here is how to test them individually so that you can have some assurance that they’re still usable.

A good month, maybe more, if you keep them in the fridge. I just test the eggs in water and make sure they don’t float if they are over two weeks past the date. If you are worried about keeping them far past the date you could boil them and that would give you a week to eat the hard boiled eggs. You can add them to salads, make egg salad, and slice them into a breakfast sandwich.

“Refrigerated raw shell eggs will keep without significant quality loss for about 4 to 5 weeks beyond the “sell by” date or about 3 weeks after you bring them home. ”

Source

I don’t eat stuff based on the sell date. If it doesn’t stink or look funny, eat it.

Farm fresh eggs have porous shells and may spoil sooner that store bought eggs, which have been sealed with Water Glass (sodium silicate, potassium silicate, or both.)

You can keep the eggs for the rest of your life, if you choose.
If you leave them exposed in a self-defrosting refrigerator for several months to a year, they will completely dehydrate. Once dehydrated, there’s nothing to spoil/rot/stink. Just be careful about shaking them – the yolk will dry out last, leaving a hard knot that will break through the shell if dropped or shaken hard.

Finding an actual dehydrated egg is a bit of a shock, sort of like those circus manikins that turn out to be real mummies.