Results 21 to 30 of about 7,411,029 (61)

Diophantine triples in a Lucas-Lehmer sequence [PDF]

, 2018
In this paper, we define a Lucas-Lehmer type sequence denoted by (Ln)1n=0, and show that there are no integers 0 < a < b < c such that ab + 1, ac + 1 and bc + 1 all are terms of the sequence. Keywords: Diophantine triples, Lucas-Lehmer sequences MSC:
Gueth, Krisztián
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Effective primality tests for some integers of the forms 𝐴5ⁿ-1 and 𝐴7ⁿ-1

, 1987
It is shown how polynomial time prime tests, which are both fast and deterministic, can be developed for many numbers of the form A r n − 1 ( r =
H. C. Williams
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UJI PRIMALITAS LUCAS-LEHMER MENGGUNAKAN PROGRAM KOMPUTER [PDF]

, 2010
Untuk mengenali bilangan-bilangan prima yang sangat besar dikembangkanlah beberapa teori uji primalitas. Masing-masing teori yang telah dikembangkan sampai saat ini belum ada yang benar-benar sempurna dalam mengenali bilangan prima.
Kelly, Swandana, Sangadji, Sangadji
core  

The Primality of N=2A3ⁿ-1

, 1972
Lehmer [3] and Reisel [7] have devised tests for determining the primality of integers of the form A2n—1. Tables of primes of these forms may be found in [7] and Williams and Zarnke [10].
H. C. Williams
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Lucas-Lehmer test

, 2014
The aim of this thesis is to explain quadratic number field theory and prove correctness of the Lucas-Lehmer primality test. A quadratic number field is a field of the form Q( √ m).
Vejpustek, Ondřej
core  

Lucas Sequences in Primality Testing

, 2014
Prime or composite? This classification determines whether or not integers can be used in digital security. One such way to begin testing an integers primality is with the Fermat test, which says that if n is a prime number and a is an integer then an-1 ≡
Karl Heimbuck (10081618)
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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  

The 25th and 26th Mersenne primes

, 1980
The 25th and 26th Mersenne primes are 2 21701 − 1 {2^{21701}} - 1 and 2 23209
Laura Nickel, Curt Noll
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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.
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