Articles
| Open Access |
https://doi.org/10.55640/
NEW METHODS FOR DETERMINING WHETHER A SUFFICIENTLY LARGE NATURAL NUMBER IS PRIME OR COMPOSITE
Jalolxon T. Nuritdinov,Bexruzbek B. Nematov , Kokand State Pedagogical InstituteAbstract
The theory of prime numbers holds an important place in mathematics and is widely applied in cryptography, algorithms, and many other fields. Determining whether large natural numbers are prime or composite requires considerable time and computational resources using traditional methods. This study introduces new algorithmic methods and approaches for identifying prime numbers, analyzing their speed, efficiency, and accuracy. These new methods are shown to be not only theoretically significant but also applicable in practical computational fields. Simplified rules for divisibility by prime numbers are provided, and a method for deriving these divisibility rules is also explained. This work will be of great importance to engineers and researchers in mathematics and computer science who work with large numbers.
Keywords
Sufficiently large natural number, prime number, numeral systems, divisibility rules.
References
Yagudayev B.Y. *In the World of Amazing Numbers*. "O'qituvchi", Tashkent, 1973, 232 pages.
Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V. *Fundamentals of Cryptography: Textbook*, 2nd edition. Moscow: Helios ARV, 2002, 480 pages.
Vasilenko O. N. *Number-Theoretic Algorithms in Cryptography*. Moscow, MCCME, 2003, 328 pages.
Article Statistics
Downloads
Copyright License
This work is licensed under a Creative Commons Attribution 4.0 International License.