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3D Math - hold positions only in a certain number of yards

I am trying to determine from a wide range of positions how to significantly narrow the list.

I currently have about 3,000 positions (x, y, z), and I want to basically keep the positions farthest from each other (I do not need to save 100 positions that are within 2 yards of each other) .

Also, to make brute force and literally make comparisons of 3000 ^ 2, does anyone have any ideas how I can narrow this list down further?

I am a little confused about how I should approach this from a mathematical point of view.

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