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The 24th mersenne prime. [PDF]

open access: yesProc Natl Acad Sci U S A, 1971
Tuckerman B.
europepmc   +1 more source

Tests for primality

open access: yesDuke Mathematical Journal, 1951
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On a Combined Primality Test

Russian Mathematics, 2022
This article studies a combined primality test for natural numbers, called \textit{L2 test}, by combining the Lucas test and the Fermat condition test. The efficiency and complexity of this test are also analyzed, and a methodology for identifying composite numbers that pass the L2 test (called L2 pseudoprimes) is presented.
Ishmukhametov, S. T.   +3 more
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Primality testing revisited

Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92, 1992
Rabin’s algorithm is commonly used in computer algebra systems and elsewhere for primality testing. This paper presents an experience with this in the Axiom* computer algebra system. As a result of this experience, we suggest certain strengthenings of the algorithm.
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Fooling Primality Tests on Smartcards

2020
We analyse whether the smartcards of the JavaCard platform correctly validate primality of domain parameters. The work is inspired by Albrecht et al. [1], where the authors analysed many open-source libraries and constructed pseudoprimes fooling the primality testing functions.
Sedlacek Vladimir   +2 more
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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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