TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

A new algorithm to find prime numbers with less memory requirements

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pp. 1213–1236Vol. 26Issue 4June 2023DOI: 10.47974/JDMSC-1629 Crossmark XML
Received:
02 Sep 2021
Accepted:
02 Mar 2022
Published Online:
21 Aug 2023
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1629
Pages:
1213–1236

Abstract

In this paper, we suggest a new approach to find any prime numbers up to a given n ∈ ℕ*. The proposed procedure does not work like a sieve and is easy to implement as it only uses assignments and subtractions which lead to improvements in memory requirements and upgradeable runtime performance. This is because, also, the algorithm suits well parallel computing. These results aim to solve several problems affecting those routines based on sieve methods, especially when large numbers are considered.

Keywords

Subject Classifications

[2010] 11A4111Y16

References

[1] Abdullah, D., Rahim, R., Apdilah, D., Efendi, S., Tulus, T., and Suwilo, S. (2018). Prime numbers comparison using sieve of Eratosthenes and Sieve of Sundaram algorithm. In Journal of Physics: Conference Series, volume 978, page 012123. IOP Publishing.
[2] Agrawal, M., Kayal, N., and Saxena, N. (2004). PRIMES is in P. Annals of mathematics, pages 781–793.
[3] Atkin, A. and Bernstein, D. (2004). Prime sieves using binary quadratic forms. Mathematics of Computation, 73(246):1023–1030.
[4] Bombieri, E. (2000). Problems of the millennium: The Riemann hypothesis. Clay Mathematics Institute.
[5] Boujnouni, M. E. (2021). A study of prime numbers distribution based on support vector domain description. Journal of Information and Optimization Sciences, 42(4):865–882.
[6] Bufalo, M., Bufalo, D., and Orlando, G. (2021). A note on the computation of the modular inverse for cryptography. Axioms, 10(2):116.
[7] Hill, L. S. (1929). Cryptography in an algebraic alphabet. The American Mathematical Monthly, 36(6):306–312.
[8] Kahn, D. (1996). The Codebreakers: The comprehensive history of secret communication from ancient times to the internet. Simon and Schuster.
[9] Lehmer, D. H. (1930). An extended theory of Lucas’ functions. Annals of Mathematics, pages 419–448.
[10] Rivest, R. L., Shamir, A., and Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2):120–126.
[11] Sergeev, I. S. (2016). On the complexity of computing prime tables on a Turing machine. arXiv preprint arXiv:1604.01154.
[12] Silverman, J. H. (2014). A friendly introduction to number theory. Pearson.
[13] Sundarayya, P. and Vara Prasad, G. (2019). A public key cryptosystem using affine Hill cipher under modulation of prime number. Journal of Information and Optimization Sciences, 40(4):919–930.
[14] Trigiante, G. and Trigiante, D. (2002). A discrete approach to the prime number theorem. The Journal of Difference Equations and Applications, 8(1):93–100.
[15] Viswanath, M. and Kumar, M. R. (2015). A public key cryptosystem using Hill’s cipher. Journal of Discrete Mathematical Sciences and Cryptography, 18(1-2):129–138.
[16] Wirian, D. J. (2009). Parallel prime sieve: Finding prime numbers. Institute of Information & Mathematical Sciences Massey University at Albany, Auckland, New Zealand.
[17] Zhang, Y. (2014). Bounded gaps between primes. Annals of Mathematics, pages 1121–1174.

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