The tumor suppressor p53 is a transcription factor that searches its cognate sites on DNA. During the search, the roles and interplay of its two DNA binding domains, the folded core domain and the disordered C-terminal domain (CTD), have been controversial. Here, we performed molecular simulations of p53 at various salt concentrations finding that, at physiological salt concentration, p53 diffuses along nonspecific DNA via rotation-uncoupled sliding with its CTD, whereas the core domain repeats dissociation and association. This is in perfect agreement with a recent single molecule experiment. In the simulation of tetrameric full-length p53, two DNA binding domains both bound to nonspecific DNA in a characteristic form at low salt concentration, whereas at physiological salt concentration, only CTD kept bound to DNA and the core domain frequently hopped on DNA. Simulations of a construct that lacks the core domain (TetCD) clarified rotation-uncoupled diffusion on nonspecific DNA. At low salt concentration, the diffusion constant due to sliding was dependent on the salt concentration, which differs from the prediction of a classic theory of transcription factors. At physiological salt concentration, it was independent of the salt concentration, in harmony with experiments. Moreover, we found that the sliding via the CTD follows the helical pitch of DNA (i.e., rotation-coupled sliding) at low salt concentration while it is virtually uncoupled to the helical pitch, a hallmark of rotation-uncoupled sliding at physiological salt concentration.