The main objective of the present paper is the detailed analysis of the electron kinetics near the Paschen's curve minimum of pulsed breakdown of nitrogen gas. Three main questions are to be answered. First, whether the breakdown curve minimum corresponds to the threshold electric field necessary for the runaway electron generation. Second, what is the role of these electrons in the vicinity of the Paschen's curve minimum. Third, what is the ionization cost near the minimum. To answer these questions, the one-dimensional model is used in which electrons are modeled using the Particle-in-Cell approach, while ions are modeled in the drift-diffusion approximation.