Applied Physics and Mathematics Annotation << Back ASYMPTOTIC OF SUMMATION ARITHMETIC FUNCTIONS, THE LIMIT FOR WHICH IS THE LAW OF NORMAL DISTRIBUTION 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. We investigate summation arithmetic functions associated with the distribution of prime numbers in the paper. Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Statements about the asymptotic behavior of the indicated functions are proved. Keywords: summation arithmetic function, asymptotically independent terms, asymptotic behavior, Mertens function, Liouville function, Mobius function, limit distribution of summation arithmetic functions, law of normal distribution. DOI: 10.25791/pfim.02.2019.600 Contacts: E-mail: znakvicvolf@mail.ru Pp. 41-45.