To find the freshest eggs at the supermarket, you can decode the numbers on the carton. The number we’re looking for is the three digit number (circled in red below). This is the ordinal date (the day of the year) the eggs were packaged (so 1 is January 1, 2 is January 2, etc.) Assuming the eggs were all handled the same way, I think you can assume that eggs packaged more recently are fresher.
Interestingly, the “use by” by date (the month/day indicated on the carton) seems less reliable. These two cartons in my refrigerator have the same packing date yet the “use by” dates are more than a week apart. In my local grocery store, I’ve seen packaging dates more than three weeks apart on the shelf. While the eggs are probably all safe to eat, I’m confident there’s a big drop in quality between these eggs. (I look for how thick/runny the whites are.)
In case you’re curious, the Pxxxx number is the plant where the eggs were packed.