Spatiotemporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. Particular attention is paid to clarifying how the statistical properties of earthquakes depend on the frictional and elastic properties of earthquake faults. It is found that as the velocity-weakening tendency of the friction force gets weaker, the system tends to be more critical, while as the velocity-weakening tendency gets stronger, the system tends to be more off critical with enhanced features of a characteristic earthquake. The model exhibits several eminent precursory phenomena prior to the large event in its spatiotemporal correlations. Preceding the main shock, the frequency of smaller events is gradually enhanced, whereas just before the main shock, it is suppressed in a close vicinity of the epicenter of the upcoming event (the Mogi doughnut). The timescale of the onset of the doughnut-like quiescence depends on the extent of the frictional instability. Under certain conditions, preceding the main shock, the apparent B value of the magnitude distribution increases significantly. The existence of such distinct precursory phenomena may open a way to the prediction of the time and the position of the upcoming large event.