We propose afiltering method to overcome memory constraints, and use the algorithm to expand much more the prime base andfind medium size primes (dozens of digits).
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, we propose a deterministic algorithm for primality testing and primes search in a giveninteger interval.
📊
Key Findings & Data:The algorithm is working; it generates a primebase by an expansion process and is appropriate for a fast search for small primes (a dozen of digits).
💡
Conclusion & Impact:We propose afiltering method to overcome memory constraints, and use the algorithm to expand much more the prime base andfind medium size primes (dozens of digits).
🔬Design:Experimental Field Trial
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we propose a deterministic algorithm for primality testing and primes search in a giveninteger interval. The algorithm use a new primality test method, which replace modulo operator with elementaryarithmetic operations, hence a better efficiency than divisibility test. The algorithm is working; it generates a primebase by an expansion process and is appropriate for a fast search for small primes (a dozen of digits). We propose afiltering method to overcome memory constraints, and use the algorithm to expand much more the prime base andfind medium size primes (dozens of digits).
🔖
Cite This Article
Mechkene, F. (2022). An Efficient Algorithm to Find All Primes in A Given Interval. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: 2, 74–77. https://ajindex.com/articles/609143
Duta, C., Gheorghe, L., Tapus, N., Framework for Evaluation and Comparison of Primality Testing Algorithms, 20th Int. Conf. on Control Systems and Science, 2015
Kumar, A., Kim, T., Lee, H., An Improved Divisibility Test Algorithm for Primality Testing, Ubiquitous Information Technologies and Applications, pp. 547–554, Y.-H. Han et al. eds., 2013
Liang, Y.D., Efficient Algorithms for Finding Prime Numbers In Introduction to Java Programming, 10th Edition, Pearson, pp. 860-866, 2015
Riesel, H., Prime Numbers and Computer Methods for Factorization, Chap. Basic Concepts in Higher Algebra, Springer Science+Business Media, LLC 2012, Modern Birkhauser
Schoof, R., Four Primality Testing Algorithms, Algorithmic Number Theory, MSRI Publications, Volume 44, 2008
Wang, X., Mathematical Foundations of Public Key Cryptography, CRC Press, pp.27-30. 2016
Yan, S. Y., Computational Number Theory and Modern Cryptography, Chap. Primality Testing, Wiley, 2017.