In our first calculations using dimensional analysis, we found the approximate value of a large number (the order of 10^61) connecting mass, age, size, minimal measurable temperature and density of the observable universe with Planck mass, time, length, temperature and density, respectively. In separate calculations, we have recalculated Planck units with a second definition of Planck mass as a mass whose Compton wavelength and gravitational radius are equals. In result, exact equation of the large number N = 5.73x10^60 has been found, connecting cosmological parameters (mass, age, size, minimal measurable temperature and density of the observable universe) and fundamental microscopic properties of the matter (Planck mass, time, length, temperature and density). Thus, a precise formulation and proof of Dirac Large Numbers Hypothesis (LNH) has been found, connecting the microworld and the macroworld. Besides, it has been found that the Planck mass represents the geometric mean of Hubble mass and mass of the observable universe. Finally, a hypothesis has been suggested for superhot superdense primordial Planck state of the matter (PSM) with Planckian density and temperature from where the universe emerged after the Big Bang.