Results 1 to 10 of about 84 (83)
A primality test for Kpⁿ⁺¹ numbers and a generalization of Safe primes and Sophie Germain primes [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we provide a generalization of Proth's theorem for integers of the form Kpⁿ⁺¹. In particular, a primality test that requires a modular exponentiation (with a proper base a) similar to that of Fermat's test without the computation of any ...
Abdelrahman Ramzy
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On the calculation of integer sequences, associated with twin primes
Lietuvos Matematikos Rinkinys, 2023 The twin primes conjecture states that there are infinitely many twin primes. While studying this hypothesis, many important results were obtained, but the problem remains unsolved.
Igoris Belovas +2 more
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New properties of divisors of natural number [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The divisors of a natural number are very important for several areas of mathematics, representing a promising field in number theory. This work sought to analyze new relations involving the divisors of natural numbers, extending them to prime numbers ...
Hamilton Brito da Silva
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Arab Journal of Basic and Applied Sciences, 2023 Lucas-Lehmer test is the current standard algorithm used for testing the primality of Mersenne numbers, but it may have limitations in terms of its efficiency and accuracy.
Moustafa Ibrahim
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مجلة بغداد للعلوم, 2023 In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test.
Yahia Awad, Ramiz Hindi, Haissam Chehade
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Recent Breakthrough in Primality Testing
Nonlinear Analysis, 2004 This paper briefly surveys the history of primality tests. The recently discovered deterministic polynomial time primality test due to Agrawal, Kayal and Saxena is presented and some improvements are shortly discussed.
R. Šleževičienė +2 more
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Toward the Unification of Physics and Number Theory [PDF]
Reports in Advances of Physical Sciences, 2019 This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure.
Klee Irwin
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An RSA Scheme based on Improved AKS Primality Testing Algorithm
MATEC Web of Conferences, 2016 In applied cryptography, RSA is a typical asymmetric algorithm, which is used in electronic transaction and many other security scenarios. RSA needs to generate large random primes.
Wu Han Wei +4 more
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Primality proving with Gauss and Jacobi sums
Journal of Telecommunications and Information Technology, 2004 This article presents a primality test known as APR (Adleman, Pomerance and Rumely) which was invented in 1980. It was later simplified and improved by Cohen and Lenstra.
Andrzej Chmielowiec
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On the resolvent of an ideal and some applications
International Journal of Mathematics and Mathematical Sciences, 2003 We give an algorithm to compute a resolvent of an algebraic variety without computing its irreducible components; we decompose the radical of an ideal into prime ideals and we test the primality of a regular ideal.
Driss Bouziane, Abdelilah Kandri Rody
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