I keep getting {{k,Ceiling[Length[newLists$109483]/2],Length[newLists$109483]};\ newLists$109483=SortBy[newLists$109483,Fitness];gg=ListPlot[newLists$\ 109483[[1]],Axes->False,PlotStyle->PointSize[0.02`]]} does not have \ appropriate bounds. >> as an error.

I copy pasted it directly. I cannot see anything happening. Could you help me?

Where does the image get stored?

How do I run this mathematica code on my machine?

I just realized that I messed up.

For $n = 4$, if you make an equilateral triangle with one point in the center I think you get $4\sqrt{3}$

@GerhardPaseman I had meant to find the minimum value for each value of $n$ not to find the value of $n$ which achieves the minimum. By the way, it is pretty easy to prove that equilateral triangle is optimal for $n = 3$.

Considering that this would essentially provide a geometric interpretation of the Basel problem, the following proof perhaps could be transformed into what you are looking for: math.chalmers.se/~wastlund/Cosmic.pdf. I am not really sure though.