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Dude, I just started a new playthrough, and I've been to about a dozen systems on this playthrough, and I discovered like 8 of them myself.
On Euclid.
The galaxy everybody starts in.
I would think that simply finishing the Atlas Quest and asking for a lush galaxy (which will send you to Eissentam) is perfectly fine. You can easily throw a rock and probably hit a dozen undiscovered systems.
Each Galaxy has 281,474,976,710,655 objects (planets/stations/atlas/portal, 12 digit hexidecimal addresses, so 12 to the power of 16).
It would take decades, if not centuries, for players to run out of new systems to discover in one galaxy, let alone 255 of them.
EDIT: Actually I think that number is # of planets, because you can input addresses and I THINK all of them are valid addresses? I've just thrown random addresses into portals before and I never saw one yet that didn't take me to a planet.
Each galaxy has about 4 trillion stars (if I remember the math correctly). If 100 million players each explored 400 systems that would still only be 1%.
Most players when they say, "my ideal planet" as posted by the OP, - it means "Paradise" or at least a clear weather lush planet that looks Earth-like or at least has a nice color scheme that isn't too tutti fruitti. And usually, they mean at the center of the galaxy, on the "edge" which would allow them to portal to a base there, then jump to the next galaxy, only having to warp once. If they aren't too picky about being RIGHT at the edge, but are ok with a planet two or three jumps from the center, it is only slightly more available in overpopulated galaxies like Euclid. But sure, if you back off *many* jumps from the center, any galaxy will have some discoverable lush clear weather planet in an undiscovered system.