Many chemical models of dense interstellar clouds predict that the majority of gas-phase elemental nitrogen should be present as N(2), with an abundance approximately five orders of magnitude less than that of hydrogen. As a homonuclear diatomic molecule, N(2) is difficult to detect spectroscopically through infrared or millimeter-wavelength transitions. Therefore, its abundance is often inferred indirectly through its reaction product N(2)H(+). Two main formation mechanisms, each involving two radical-radical reactions, are the source of N(2) in such environments. Here we report measurements of the low temperature rate constants for one of these processes, the N + CN reaction, down to 56 K. The measured rate constants for this reaction, and those recently determined for two other reactions implicated in N(2) formation, are tested using a gas-grain model employing a critically evaluated chemical network. We show that the amount of interstellar nitrogen present as N(2) depends on the competition between its gas-phase formation and the depletion of atomic nitrogen onto grains. As the reactions controlling N(2) formation are inefficient, we argue that N(2) does not represent the main reservoir species for interstellar nitrogen. Instead, elevated abundances of more labile forms of nitrogen such as NH(3) should be present on interstellar ices, promoting the eventual formation of nitrogen-bearing organic molecules.