Strong Primality Tests that are Not Sufficient
نویسندگان
چکیده
منابع مشابه
3.1 Classical Primality Tests
Andrew V. Sutherland In this lecture, we consider the following problem: given a positive integer N , how can we efficiently determine whether N is prime or not? This question is intimately related to the problem of factoring N . Without a method for determining primality, we have no way of knowing when we have completely factored N . This is a serious issue for probabilistic factorization algo...
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In 1980, L. Adleman, C. Pomerance, and R. Rumely invented the first cyclotomic primality test, and shortly after, in 1981, a simplified and more efficient version was presented by H.W. Lenstra for the Bourbaki Seminar. Later, in 2008, Rene Schoof presented an updated version of Lenstra’s primality test. This thesis presents a detailed description of the cyclotomic primality test as described by...
متن کامل2.1 Classical Primality Tests
In this lecture, we consider the following problem: given a positive integer N , how can we efficiently determine whether N is prime or not? This question is intimately related to the problem of factoring N ; without a method for determining primality, we have no way of knowing when we have completely factored N . This is an important issue for probabilistic factorization algorithms such as ECM...
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The first deterministic polynomial-time algorithm for primality testing by Agrawal, Kayal, and Saxena [Agrawal et al. 02] has been epoch-making. On the other hand, some previously known primality (or pseudoprimality) tests are still of interest not only because they are faster practically but also because they offer interesting mathematical objects such as pseudoprimes. The aim of this paper is...
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Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1982
ISSN: 0025-5718
DOI: 10.2307/2007637