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We introduce new analytical approximations of the minimum electrostatic energy configuration of n electrons, E(n), when they are constrained to be on the surface of a unit sphere. Using 453 putative optimal configurations, we searched for approximations of the form where g(n) was obtained via a memetic algorithm that searched for truncated analytic continued fractions finally obtaining one with Mean Squared Error equal to for the model of the normalized energy (). Using the Online Encyclopedia of Integer Sequences, we searched over 350,000 sequences and, for small values of n, we identified a strong correlation of the highest residual of our best approximations with the sequence of integers n defined by the condition that is a prime. We also observed an interesting correlation with the behavior of the smallest angle , measured in radians, subtended by the vectors associated with the …