If someone wants to get to elite rank quickly (or, well, 'quickly' may not be the right term), head to the neutron fields in the direction of Sag A*. That's a perfectly legitimate way of doing so, and many have done so. You don't have to do that, you can go elsewhere and explore, or, if you are really bold, go on a single epic voyage. If you do that latter, make sure to take pictures!
But whatever way you do it, its not so much a question of systems as a question of how much real-life actual time you want to put into playing a video game. I made several long trips to the Perseus and Outer Arms, fairly prosaic trips compared to other explorers, and never got more than a 21 kly from the bubble. It took me several months of real time to do all of this. I did take breaks from Elite to play other games, but in the end I have cracked 1000 hours of total play time.
Getting to elite in exploration is not intrinsically difficult, it just takes a lot of time. It's more a question of patience and persistence than anything else. I found it to be very rewarding once I cracked that barrier, and frankly, I am proud of my accomplishment (as silly as that sounds, its video game after all). It was extremely nerve wracking coming back to the bubble on that last trip to the rim, wondering what would happen if I was interdicted. Very nerve wracking and adrenaline pounding. I had spent two months on that last trip, I wasn't sure I had enough to make elite, but I knew there was a chance I could lose it all in seconds. It was all the excitement anyone can ask for in a game. I'm glad I did it.
But I would never do it again.
It's such a massive time sink. A year ago I was excited about also being able to play No Man's Sky. Now, I'm not so sure.
To actually answer the question, though, the number of systems I visited on my exploratory trips was around 6000.
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If you wanna be an explorer the rank is only a nice thing to show off. A true explorer doesnt farm neutron fields. He doesnt deliberately visit every system with an Earth like that is mentioned on the forums.
A true explorer explores anyway they like.