BUILDING OF THE MODEL

With a similar reasoning we ask ourselves, how many prime numbers exist by ranks of number of digits, under the assumption of order in the "positional notation" or "the relative value of the figures", developed by the hindu (beginning of VI century BC) and recognized as one of the major advances of mathematics, as the science of measurement and order.

The formal procedure developed is:

Definition: If

	where:
	: :
in short the formula becomes:
Convergence: the series is convergent because
In other words exist
Monotonicity:

The empirical procedure developed under this method shows the following brief table by calculating the sum of the reciprocals in numerical figures:

n	Dig	1/dig	CRAA - 2
0	4	0,250000000000000
1	21	0,047619047619048	0,297619047619048
2	143	0,006993006993007	0,304612054612055
3	1061	0,000942507068803	0,305554561680858
4	8363	0,000119554315437	0,305674135996295
5	68906	0,000014512524308	0,305688648520603
6	586081	0,000001706248795	0,305690354769398
7	5096876	0,000000196198613	0,305690550968011
8	45086079	0,000000022179795	0,305690573147806
9	404204977	0,000000002473992	0,305690575621798
10	3663002302	0,000000000273000	0,305690575894798
11	33489857205	0,000000000029860	0,305690575924658
12	308457624821	0,000000000003242	0,305690575927900

The result of the convergent series is a constant, a constant named CRAA-2 (see THE MATHEMATICAL CONSTANT OF AGUILAR-ACHA, Ciencia y Computación, EL DIARIO, 22/VII/99, La Paz-Bolivia).

NUMERICAL RESULT

This new Aguilar-Acha's constant, CRAA-2, is originated in the former set of: a formal definition, expressions and formulas and construction of the table up to 1013 decimal digits and of the primes comprised within each rank, associated to the advancement of the study of the theory of numbers, which represents to be the infinite value:

CRRA-2 = 0,3056905759...

CONCLUSION

The constant CRAA-2 is thus obtained and preliminary verifyied. In measurement terms this result suggests and help us in the decoding of primes' laws or rules related to its important regularities and is worthy of our attention concerning the outstanding and most important prime numbers, as objects or autonomous elements, in appearance just refractory to any kind of relations or regularities.

APPLICATIONS

Remembering that a beautiful theorem states that: "all numbers can be written as a product of primes", already demonstrated by other mathematicians, the constant CRAA-2 help us to prove the conjecture of scarcity of the primes in the development of its series and the density or distribution of primes. Which, undoubtedly, is of great importance for the study of the shape and construction of the structure of the mathematical science.

Also, in applied mathematics, to build algorithms for the calculation of very long figures and the processing of chains, with precision and high security in computing machines with high capacity and speed, to solve many complex problems, perform investigations, notable classifications and hierarchizations, etc. useful to judge numerical propositions on the theory of numbers and other branches of pure and applied mathematics and related sciences.

REFERENCES
R. Aguilar-Acha, La Constante de Aguilar-Acha, Ciencia y Computación, EL DIARIO, La Paz-Bolivia.
R. Aguilar-Acha, Decoding the Secrets of the Law of Primes in the Theory of Numbers, www.bolivialinux.com (2001)
G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, Oxford Science Publications, (1979)
W.J. LeVeque,Fundamentals of Number Theory, New York, Dover, (1996)

Further information: cellular 775-22299 web site www.telecel.com.bo, e-mail: raguilar40@starmedia.com or raguilar40@terra.com or telephone (591-2)-2485559, La Paz-Bolivia, South America (All rights reserved).

L.P. 12/X/01.