THE LAW OF SCALING FOR LARGE NUMBERS.

The paper solves the problem of mathematical derivation of large numbers formulated in 1985 by P.K.W. Davis [1]. The scaling law of large numbers is derived. The scaling law provides a new method for obtaining large numbers from dimensionless constants. It complements the well-known method based on the ratios of dimensional physical quantities. The scaling law of large numbers shows that large numbers of scales 10^39, 10^40, 10^61, 10^122 are only a part of the complete family of large numbers. Large numbers are supplemented by new large numbers of scales 10^140, 10^160, 10^180, which are naturally derived from the fundamental parameters of the observable Universe. New coincidences of ratios of dimensional quantities on scales 10^140, 10^160, 10^180 are found. It is shown that large numbers of different scales are functionally related to each other. The primary large number D20 = (αDo) ^ (1/2) = 1.74349... x 10 ^ 20, from which large numbers of other scales are formed according to a single law, is chosen on the scale of 10 ^ 20. The primary large number D20 = 1.74349... x 10 ^ 20 consists of two dimensionless constants: the fine structure constant alpha and the Weyl number Do = 4.16561... x 10 ^ 42. Coincidences of the ratios of dimensional quantities with large numbers on the scales of 10 ^ 160 and 10 ^ 180 made it possible to derive simple and beautiful formulas for calculating the cosmological constant Ʌ.