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This paper considers a probabilistic-analytical approach to determiningasymptotics of prime objects on the initial interval of the natural series. Theauthor proposes a new method based on the construction of a probability space.An arithmetic function is considered that counts the number of prime objects(for example, prime numbers, twin primes, prime values of polynomials) on agiven probability space. The properties of this arithmetic function are proved.Based on these properties, the specified probabilistic-analytical approach isconstructed. As examples of the application of this approach, the definition ofthe asymptotics of the number of prime twins and pairs of prime numbers thatadd up to an even number (based on Goldbach's conjecture) is considered. It isshown that the proposed method allows one to obtain asymptotic estimates thatcoincide with the known conjecturea of prime number theory. This approach opensup new possibilities for studying conjectures about prime numbers, offering analternative way to prove them based on probabilistic methods.

Probabilistic analytical approach to determining the asymptotics of prime objects on the initial interval of the natural series