Results 151 to 160 of about 195 (180)
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A New Probabilistic Primality Test
Journal of Mathematical Sciences, 2020In 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
1993A 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
1995The 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, 2020Shamil Ishmukhametov
exaly
Primality and identity testing via Chinese remaindering
Journal of the ACM, 2003Manindra Agrawal
exaly
Inefficacious Conditions of the Frobenius Primality Test and Grantham's Problem
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2008Naoyuki Shinohara
exaly