What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J. J. Thomson posed this question in 1904. For N<=112, numerical methods have found apparent global minimum-energy configurations; but the number of local minima appears to grow exponentially with N, making many such methods impractical. Here we describe a topological/numerical procedure that we believe gives the global energy minimum lattice configuration for N of the form N = 10\(m2+n2+mn\)+2 ( m, n positive integers). For those N with more than one lattice, we give a rule to choose the minimum one.