Applied Physics and Mathematics Annotation << Back ASYMPTOTIC OF SOME SUMMATION ARITHMETIC FUNCTIONS V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of primes has acquired important practical significance, since it is directly related to the reliability of the so-called public-key cryptographic systems. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of decomposing into prime factors of large natural numbers. In this paper, we investigate summation arithmetic functions associated with the distribution of prime numbers. The paper compares the asymptotic of the expressions and and The asymptotic of summering arithmetic functions (n,p – respectively, positive and prime numbers) are determined if the asymptotes of summation arithmetic functions are known, respectively. Keywords: arithmetic function, summation arithmetic function, asymptotic, asymptotic upper bound, Abel summation formula, Euler-Macleron formula, Chebyshev function, Möbius function, number of positive divisors of the natural series. DOI: 10.25791/pfim.01.2019.500 Contacts: E-mail: znakvicvolf@mail.ru Pp. 49-53.