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On the Lucas and Lehmer sequences in Dedekind domain
In this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the primitive divisor results for such sequences in function ...
Xiumiei Li, Min Sha, Giulio Peruginelli
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Improvements to Lucas-sequence modular square roots and primality testing [PDF]
Lucas sequences are a helpful tool in mathematical and cryptographic calculations, providing in particular an efficient way to exponentiate in a quotient ring $R[x]/(x^2 - Px + Q)$. As with exponentiation in other finite rings and fields, we can use the
Mike Hamburg
core
### Título"Otimização do Teste de Lucas-Lehmer para Números Primos de Mersenne: UmaAbordagem Eficiente Utilizando gmpy2" ### ResumoEste artigo apresenta uma otimização significativa do teste de Lucas-Lehmer para númerosde Mersenne, utilizando a ...
Marlon Fernando Polegato
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A Treatise on the Theory of Mersenne Numbers and Primality Testing
This thesis explores Mersenne numbers, numbers of the form $2^p-1$ where $p$ is prime. We are particularly concerned with when such numbers are themselves prime.
Robeson, Tanner
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Primality Tests and Prime Certificate
This note presents a formalisation done in Coq of Lucas-Lehmer test and Pocklington certificate for prime numbers. They both are direct consequences of Fermat little theorem. Fermat little theorem is proved using elementary group theory and in particular
Théry, Laurent
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A Lucas-Lehmer Primality Test for the Belphegor Numbers
The Fibonacci QuarterlyHugh C Williams
exaly +2 more sources
Existence of Primitive Divisors of Lucas and Lehmer Numbers
Journal Fur Die Reine Und Angewandte Mathematik, 2001 Article dans revue scientifique avec comité de lecture.We prove that for~${n>30}$, every~$n$-th Lucas and Lehmer number has a primitive divisor.
BILU, Yuri +2 more
exaly +2 more sources