“…Already J. J. Thomson (discovering electron in 1897) suggested the problem of finding such configurations on the sphere, and the answer has been known for N = 2, 3, 4 for more than 100 years, but for N = 5 the solution was obtained only quite recently [4]. In one-dimensional case T, J, Stieltjss studied the problem with logarithmic interaction and found its connection with zeros of orthogonal polynomials on the corresponding interval, see [2], [3]. However, the problem of finding minimal energy configurations on two-dimensional sphere for any N and power interaction (sometimes it is called the seventh problem of S. Smale, it is also connected with the names of F. Risz and M. Fekete) was completely solved only for quadratic interaction (see [5], [7], [8] and review [6]).…”