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For all the newfags around here, what you're seeing is an ancient glitch known as "Bad Egg" or "Mystery Egg" as of Gen 6.
It's basically corrupted data that can overwrite itself in other pokemon and "spread", turning any pokemon near it into a Bad Egg and cycle repeats until all pokemon are affected. It initially started as a anti hack system back in Gen 3 as in if you tried to hack mons in those games and use Game Sharks, you would get a Bad Egg, it was GF's way of punishing cheaters. As for what happened if you tried to hatch it, it would crash your game and eventually corrupt your file. That is if you messed around with it. The best thing you could do was to deposit it in a empty box and forget about it.
This glitch still remained in Gen 4 and 5, it somewhat disappeared in 6, but was shortly replaced by the "Mystery Egg", which you could only get via Wonder Trade. But it was super rare, like a 1% chance you would ever encounter it I know this since I've spent weeks on end on WT and never once encountered one.
Also, fun fact, in Gen 3, the Egg if hatched successfully (or not, I can't remember), it would appear as a golden Bulbasaur in your party summary.
