Results 21 to 30 of about 100 (72)

New primality criteria and factorizations of 2^{𝑚}±1

, 1975
A collection of theorems is developed for testing a given integer N for primality. The first type of theorem considered is based on the converse of Fermat’s theorem and uses factors of N − 1 N - 1 .
J. L. Selfridge, D. H. Lehmer, John Brillhart   +2 more
core   +1 more source

Developments on primality tests based on linear recurrent sequences of degree two [PDF]

, 2022
Some probabilistic primality tests, like the strong Lucas test that is part of the widely used Baillie-PSW test, are defined through linear recurrent sequences.
Simone Dutto
core  

A Proof of the Lucas-Lehmer Test and its Variations by Using a Singular Cubic Curve

, 2018
We give another proof of the Lucas-Lehmer test by using a singular cubic curve. We also illustrate a practical way to choose a starting term for the Lucas-Lehmer-Riesel test by trial and error. Moreover, we provide a nondeterministic test for determining
Küçüksakallı, Ömer
core  

A really trivial proof of the Lucas-Lehmer primality test

, 1993
In the paper [1] Rosen gave a beautiful and elementary proof of the Lucas-Lehmer primality test for Mersenne numbers, i.e. those of the form Mp = 2p - 1.
Bruce, J.W.
core  

Iterated digit sums, recursions and primality [PDF]

, 1997
summary:We examine the congruences and iterate the digit sums of integer sequences. We generate recursive number sequences from triple and quintuple product identities.
Kang, Soon-Yi, Ericksen, Larry
core   +1 more source

BIQUADRATIC RECIPROCITY AND A LUCASIAN PRIMALITY TEST

, 2008
. Let {sk,k ≥ 0} be the sequence defined from a given initial value, the seed, s0, by the recurrence sk+1 = s2 k − 2,k ≥ 0. Then, for a suitable seed s0, thenumberMh,n = h · 2n − 1(whereh<2n is odd) is prime iff sn−2 ≡ 0modMh,n.
Pedro Berrizbeitia, T. G. Berry
core  

Accuracy increase in determination composite number by probabilistic primality tests [PDF]

, 2005
Accuracy increasing problem became important after there were found so-called numbers of Carmichael, and it became evident that the simplest primality test based on Fermat’s Little Theorem failed.
BALABANOV, A., AGAFONOV, A.
core  

Prime numbers and primality test

, 2018
Orientador: Ricardo Miranda MartinsDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação CientíficaResumo: Nesta dissertação estudamos números inteiros, suas propriedades e congruências.
Paiva, Glaucia Innocencio de Jesus Paulo, 1985-
core  

Lehmer Numbers with at Least 2 Primitive Divisors [PDF]

, 2007
In 1878, Lucas \cite{lucas} investigated the sequences $(\ell_n)_{n=0}^\infty$ where $$\ell_n=\frac{\alpha^n-\beta^n}{\alpha-\beta},$$ $\alpha \beta$ and $\alpha+\beta$ are coprime integers, and where $\beta/\alpha$ is not a root of unity.
Juricevic, Robert
core  

Determination of the primality of 𝑁 by using factors of 𝑁²±1

, 1976
Algorithms are developed which can be used to determine the primality of a large integer N when a sufficient number of prime factors of N 2 + 1 {N^2} + 1 are known. A
J. S. Judd, H. C. Williams
core   +1 more source