منابع مشابه
Sums of Prime Divisors and Mersenne Numbers
The study of the function β(n) originated in the paper of Nelson, Penney, and Pomerance [7], where the question was raised as to whether the set of Ruth-Aaron numbers (i.e., natural numbers n for which β(n) = β(n+ 1)) has zero density in the set of all positive integers. This question was answered in the affirmative by Erdős and Pomerance [5], and the main result of [5] was later improved by Po...
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Pseudo-random numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of a Mersenne prime. These generators are based on “almost primitive” trinomials, that is trinomials ha...
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In this correspondence, it is shown that Legendre sequences of period p can be explicitly represented using the trace function defined on the finite field with 2n elements, whenever p = 2n 1 is prime for some R 2 3.
متن کاملOn the largest prime factor of the Mersenne numbers
Let P (k) be the largest prime factor of the positive integer k. In this paper, we prove that the series ∑ n≥1 (log n)α P (2n − 1) is convergent for each constant α < 1/2, which gives a more precise form of a result of C. L. Stewart of 1977.
متن کاملGaussian Mersenne and Eisenstein Mersenne primes
The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1914
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1914-02547-9