Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back Data Structure and Algorithms Based on it for Factorizing Natural Numbers in a Given Range D.V. POLYAKOV, E.U. VELEGURINA The article proposed a data structure based on a subsequence of the natural series containing all prime numbers. This structure allows factorization of numbers from a given range in the worst case in logarithmic time, in the best case in the factorization length, and checking for primality in constant time. The paper provides an estimate of the asymptotic complexity of all proposed algorithms. The work also presents mathematical model on the basis of which the proposed data structure is built. Within the framework of the given mathematical model, a subsequence of the natural series is introduced into consideration, containing all prime numbers. Examples of members of the considered subsequence are given and their growth is assessed in comparison with the growth of a number of natural and prime numbers. Keywords: higher arithmetic, number theory, factorization, primality test, prime number, data structure, algorithm, asymptotic complexity, index array, doubly linked list. DOI: 10.25791/pribor.9.2023.1442 Pp. 47-62.