Results 101 to 110 of about 463 (134)

Primality testing

, 2008
Prime numbers have a very simple definition, but they inspire an abundance of interesting and complex theory. Originally a topic of interest only to pure mathematicians, primes have found an important practical role in our modern technological world ...
Jeff Wehrwein (14101011)
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Combinatorial primality test

ACM Communications in Computer Algebra, 2020
In 1879, Laisant-Beaujeux gave the following result without proof: If n is a prime, then [EQUATION] This paper provides proofs of the result of Laisant-Beaujeux in two cases explicitly: (1) If an integer of the form n = 4k + 1, k > 0 is prime, then ([EQUATION]) and (2) If an integer of the form n = 4k + 3, k ≥ 0 is prime, then ...
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On a Modification of The Lucas Primality Test

Lobachevskii Journal of Mathematics, 2023
Let \(F_n\) be the Fibonacci series defined by \(F_0 = 0\), \(F_1 = 1\), and \(F_{n+2} = F_n + F_{n+1}\). Set \(e(n) = (n/5)\), where \((\cdot/5)\) is the usual Legendre symbol. The classical Lucas primality test is based on the following result: If \(n > 5\), then \(F_{n-e(n)} \equiv 0 \pmod n\).
Ishmukhametov, Sh., Antonov, N., Mubarakov, B.   +2 more
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Pseudocubes and Primality Testing

2004
The recent ideas of Agrawal, Kayal, and Saxena have produced a milestone in the area of deterministic primality testing. Unfortunately, their method, as well as their successors are mainly of theoretical interest, as they are much too slow for practical applications.
Pedro Berrizbeitia, Siguna Müller, Hugh C. Williams   +2 more
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A New Probabilistic Primality Test

Journal of Mathematical Sciences, 2020
In this paper, a new efficient general probabilistic primality test is presented. The main idea is as follows. Let \(n > 1\) be an odd positive integer. First, it is checked whether \(n\) can be represented as \(n = a^b\), where \(a\) and \(b\) are integers \(\ge 2\).
Moshonkin, A. G., Khamitov, I. M.
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Primality testing with Lucas functions

1993
A generalization of Fermat's Little Theorem is derived by using Lucas functions. This generalization yields new classes of pseudoprimes and can be used to improve some well-known primality tests.
Rudolf Lidl, Winfried B. Müller
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A primality test for Fermat numbers

1995
The paper gives a primality criterion for Fermat numbers \(F_n=2^{2^n}+1\) \(\left(n=0,1,2,\ldots\right)\). The author proves the following theorem. Let \(k\) and \(n\) be fixed positive integers such that \(0< k\leq [\log n/\log_2]\) and \(n>1\). The Fermat number \(F_k\) is prime if and only if \(F_k\) does not divide \(T\left(2^{n-1}\right)\), where
Grytczuk, A., Grytczuk, J.
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On the Number of Witnesses in the Miller–Rabin Primality Test

Symmetry, 2020
Shamil Ishmukhametov
exaly  

A New Primality Test for Natural Integers

Russian Mathematics, 2022
exaly  

Primality tests, linear recurrent sequences and the Pell equation

Ramanujan Journal, 2021
Simone Dutto, Nadir Murru, Murru Nadir   +2 more
exaly