The thermodynamics of nucleic acid processes is heavily affected by the electric double layer of microions around the polyions. We focus here on the Coulombic contribution to the salt-polyelectrolyte preferential interaction (Donnan) coefficient, and we report extremely accurate analytical expressions valid in the range of low salt concentration (when polyion radius is smaller than the Debye length). The analysis is performed at the Poisson-Boltzmann level, in cylindrical geometry, with emphasis on highly charged polyions (beyond "counterion condensation"). The results hold for any electrolyte of the form z(-):z(+). We also obtain a remarkably accurate expression for the electric potential in the vicinity of the polyion.