Results 1 to 10 of about 229 (32)
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 +3 more sources
Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 𝐴.3ⁿ±1 [PDF]
Proceedings of the American Mathematical Society, 1999 Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form A .3 n ± 1 A.3^n \pm 1 . The test for A .3 n − 1 A.3^n-1 is a minor improvement on a test derived ...
Berrizbeitia, Pedro, Berry, T. G.
openaire +1 more source
Orthogonal polynomials and Riesz bases applied to the solution of Love's equation [PDF]
, 2016 In this paper we reinvestigate the structure of the solution of a well-known Love’s problem, related to the electrostatic field generated by two circular coaxial conducting disks, in terms of orthogonal polynomial expansions, enlightening the role of the
BERSANI, Alberto Maria +1 more
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A simpler alternative to Lucas–Lehmer–Riesel primality test [PDF]
, 2023 This paper investigates application of Morrison primality test to numbers of $k \cdot 2^n-1$ form and finds a simple general formula, which is equivalent to Lucas–Lehmer and Lucas–Lehmer–Riesel primality ...
Pavel Atnashev
core
A primality test for Kp^n+1 numbers [PDF]
, 2015 In this paper we generalize the classical Proth's theorem and the Miller-Rabin test for integers of the form N = Kpn +1. For these families, we present variations on the classical Pocklington's results and, in particular, a primality test whose ...
Grau, José María +2 more
core +3 more sources
Algorithms and the mathematical foundations of computer science [PDF]
, 2016 The goal of this chapter is to bring to the attention of philosophers of mathematics the concept of algorithm as it is studied incontemporary theoretical computer science, and at the same time address several foundational questions about the role this ...
Dean, Walter
core +1 more source
On the emergence of the Quanta Prime sequence
Arab Journal of Basic and Applied SciencesThis paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
doaj +1 more source
Arab Journal of Basic and Applied SciencesMersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Ibrahim
doaj +1 more source
Deterministic elliptic curve primality proving for a special sequence of numbers
, 2013 We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm uses O(log N)
Everest +5 more
core +2 more sources
On Taking Square Roots without Quadratic Nonresidues over Finite Fields
, 2009 We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary.
Sze, Tsz-Wo
core +2 more sources