Applied Physics and Mathematics Annotation << Back ASYMPTOTICS OF SUMS OF PRIME 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 importance, since it is directly related to the reliability of the so-called cryptographic systems with a public key. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of factorization of large natural numbers. In this paper, we investigate the asymptotic problem of the sums of functions of primes. It is directly related to the problem of the distribution of primes. The aim of this paper is to obtain the remainder term and consider various examples of determining the asymptotic behavior of the sums of prime functions. Also, the necessary and sufficient conditions for the existence of these asymptotics are proved in the paper. Keywords: arithmetic function, adder function, asymptotic prime law, Riemann conjecture, Abel’s formula. DOI: 10.25791/pfim.04.2020.1168 Pp. 23-29.