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Vladimir Pevnev
Oles Yudin
Peter Sedlaček
Nina Kuchuk


The current stage of scientific and technological development entails ensuring information security across all domains of human activity. Confidential data and wireless channels of remote control systems are particularly sensitive to various types of attacks. In these cases, various encryption systems are most commonly used for information protection, among which large prime numbers are widely utilized. The subject of research involves methods for generating prime numbers, which entail selecting candidates for primality and determining the primality of numbers. The subject of research involves methods for generating prime numbers, which choice selecting candidates for primality and determining the primality of numbers. The objective of the work is the development and theoretical justification of a method for determining the primality of numbers and providing the results of its testing. The aim to address the following main tasks: analyze the most commonly used and latest algorithms, methods, approaches, and tools for primality testing among large numbers; propose and theoretically justify a method for determining primality for large numbers; and conduct its testing. To achieve this aim, general scientific methods have been applied, including analysis of the subject area and mathematical apparatus, utilization of set theory, number theory, fields theory, as well as experimental design for organizing and conducting experimental research. The following results have been obtained: modern methods for selecting candidates for primality testing of large numbers have been analyzed, options for generating large prime numbers have been considered, and the main shortcomings of these methods for practical application of constructed prime numbers have been identified. Methods for determining candidates for primality testing of large numbers and a three-stage method for testing numbers for primality have been proposed and theoretically justified. The testing conducted on the proposed primality determination method has demonstrated the correctness of the theoretical conclusions regarding the feasibility of applying the proposed method to solve the stated problem. Conclusions. The use of a candidate primality testing strategy allows for a significant reduction in the number of tested numbers. For numbers of size 200 digits, the tested numbers is reduced to 8.82%. As the size of the tested numbers increases, their quantity will decrease. The proposed method for primality testing is sufficiently simple and effective. The first two stages allow for filtering out all composite numbers except for Carmichael numbers. In the first stage, using the first ten prime numbers filters out over 80 percent of the tested numbers. In the second stage, composite numbers with factors greater than 29 are sieved out. In the third stage, Carmichael numbers are sieved out. The test is polynomial, deterministic, and unconditional.

Article Details

How to Cite
Pevnev , V. ., Yudin , O. ., Sedlaček , P. ., & Kuchuk , N. . (2024). METHOD OF TESTING LARGE NUMBERS FOR PRIMALITY. Advanced Information Systems, 8(2), 99–106.
Methods of information systems protection
Author Biographies

Vladimir Pevnev , National Aerospace University “Kharkiv Aviation Institute”, Kharkiv

Doctor of Sciences (Engineering), Associate Professor, Professor at the Department of Computer Systems, Networks and Cybersecurity

Oles Yudin , National Aerospace University “Kharkiv Aviation Institute”, Kharkiv

PhD student of the Department of Computer Systems, Networks and Cybersecurity

Peter Sedlaček , University of Žilina, Žilina

PhD in Computer Sciences, Assistant Professor of the Department of Informatics, Faculty of Management Science and Informatics

Nina Kuchuk , National Technical University "Kharkiv Polytechnic Institute", Kharkiv

Doctor of Technical Sciences, Professor, Professor of Computer Engineering and Programming Department


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