Discovered periodic sublimation activity on four main-belt primitive asteroids led us to conclusions about possible origin of those and similar bodies (or their parent bodies) near or beyond the snow line in the early Solar System making incorporated in them a considerable water ice stock. Water differentiation of the bodies owing to 26A1 decay and their internal thermal evolution might have created conditions for water soluble organics and prebiotic compounds formation. Subsequent longtime periodic changing temperature and other physico-chemical parameters (due to spinning and moving around the Sun) in the near-surface layers of primitive asteroids have led probably to formation of more complex organic compounds of astrobiological significance.