While the initial overwhelming hype train that was Pokemon GO has undoubtedly slowed down a little, it doesn't appear to be going anywhere soon. As the developers at Niantic and The Pokemon Company knuckle down on new features, such as new Pokemon as well as better ways to find nearby monsters. While some may have caught the 142 currently available Pokemon, many of us are still working through them, struggling to find the rarer ones out there. To do that without traveling all over the world, a lot of players have been relying on 10K eggs, that often deliver rarer Pokemon than you would otherwise be able to obtain, as well as a large amount of Stardust and Candy for that respective monster, making it easier to level up and evolve said monster.
These 10K eggs are rare commodities for a lot of players, and while they take longer than any other egg to hatch, the wait is often worth it. So much so that many users have been experimenting with near-certain ways of getting their hands on more of them. One such method is to make sure that you have the space for more eggs. This involves getting rid of all your 2K and 5K eggs, with the odds being that if you have more space for eggs when you hit a PokeStop, the likelihood of landing a 10K egg or two is higher than if you had less room. The pattern in which you visit PokeStops may also be a factor, with users reporting that more unique visits will help, for instance if you visit the same PokeStops over and over again quite frequently, the game appears to be less likely to drop a 10K egg. The same goes for landmarks and historically-rich areas, as these are apparently more likely to drop better eggs as well, but this theory has yet to be proven.
This seems to be the case for a lot of these theories, but it appears as though looping your PokeStops across a two-hour time period with a lot of space for more eggs appears to be the best way of getting more 10K eggs. Being of a higher level appears to make no difference whatsoever, and just as it has been throughout the history of the main Pokemon games on the Game Boy and DS systems, the stats and appearances of certain special items is often shrouded in mystery.