Results 11 to 20 of about 37,491 (303)
On the Eight Levels theorem and applications towards Lucas-Lehmer primality test for Mersenne primes, I [PDF]
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
doaj +2 more sources
Fooling primality tests on smartcards [PDF]
IACR Cryptology ePrint Archive, 2020 We analyse whether the smartcards of the JavaCard platform correctly validate primality of domain parameters. The work is inspired by the paper Prime and prejudice: primality testing under adversarial conditions, where the authors analysed many open ...
Vladimir Sedlacek +2 more
semanticscholar +3 more sources
Strengthening the Baillie-PSW primality test [PDF]
Mathematics of Computation, 2020 The Baillie-PSW primality test combines Fermat and Lucas probable prime tests. It reports that a number is either composite or probably prime. No odd composite integer has been reported to pass this combination of primality tests if the parameters are ...
Robert Baillie, A. Fiori, S. Wagstaff
semanticscholar +2 more sources
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
doaj +3 more sources
Direct Product Primality Testing of Graphs is GI-hard [PDF]
Theoretical Computer Science, 2020 We investigate the computational complexity of the graph primality testing problem with respect to the direct product (also known as Kronecker, cardinal or tensor product). In [1] Imrich proves that both primality testing and a unique prime factorization
L. Calderoni, L. Margara, M. Marzolla
semanticscholar +3 more sources
Computation of the ω-primality and asymptotic ω-primality with applications to numerical semigroups
, 2013 We give an algorithm to compute the ω-primality of finitely generated atomic monoids. Asymptotic ω-primality is also studied and a formula to obtain it in finitely generated quasi-Archimedean monoids is proven.
J. I. García-García +2 more
semanticscholar +2 more sources
, 2000 In this study, prime numbers and primality, which IS one of the most important topics in number theory is analyzed.Subject of primality of a number has been the focus of many scientific studies and several different theories has been developed for many years. Based on these theorems, primality of large numbers has been investigated.
Tepeli, Murat
openaire +3 more sources
On the primality and elasticity of algebraic valuations of cyclic free semirings [PDF]
International journal of algebra and computation, 2022 A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number $\alpha$, the additive monoid $M_\alpha$ of the evaluation semiring $\mathbb{N}_0[\alpha]$
Yanan Jiang, Bangzheng Li, So-Fan Zhu
semanticscholar +1 more source
Primality of weakly connected collections of cells and weakly closed path polyominoes [PDF]
Illinois Journal of Mathematics, 2021 In this paper we study the primality of weakly connected collections of cells, showing that the ideal generated by inner 2-minors attached to a weakly connected and simple collection of cells is the toric ideal of the edge ring of a weakly chordal ...
Carmelo Cisto, F. Navarra, R. Utano
semanticscholar +1 more source
Primality of closed path polyominoes [PDF]
Journal of Algebra and its Applications, 2020 In this paper, we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zig-zag walks ...
Carmelo Cisto, F. Navarra
semanticscholar +1 more source