Results 91 to 100 of about 1,108 (208)
Dimorphic Mersenne numbers and their applications
, 2022 The Mersenne primes are primes which can be written as some prime power of 2 minus 1. These primes were studied from antiquity in that their close connection with perfect numbers and even to present day in that their easiness for primality test. In this paper, we introduce the dimorphic Mersenne numbers as a degenerate version of the Mersenne numbers ...
Kim, Taekyun, Kim, Dae san
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Batched ranged random integer generation
Software: Practice and Experience, Volume 55, Issue 1, Page 155-169, January 2025.Summary Pseudorandom values are often generated as 64‐bit binary words. These random words need to be converted into ranged values without statistical bias. We present an efficient algorithm to generate multiple independent uniformly‐random bounded integers from a single uniformly‐random binary word, without any bias.
Nevin Brackett‐Rozinsky, Daniel Lemire
wiley +1 more source
On the number of divisors of Mersenne numbers
13 pages, 5 figures, 2 tables; v4: incorporated editorial ...
Kovač, Vjekoslav, Luca, Florian
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AIP Advances, 2020 The need for hardware random number generators (HRNGs) that can be integrated in a silicon (Si) complementary-metal–oxide–semiconductor (CMOS) platform has become increasingly important in the era of the Internet-of-Things (IoT).
Kouta Ibukuro +9 more
doaj +1 more source
On Mersenne’s number 𝑀₁₉₉ and Lucas’s sequences [PDF]
Bulletin of the American Mathematical Society, 1947 On July 27, 1946 the writer finished calculating the 198th remainder of the Lucasian sequence 3, 7, 47, • • • as applied to the 60-digit Mersenne number 2 1 9 9 -1=80346 90221 29495 13777 09810 46170 ...
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Primality-testing Mersenne numbers
, 1983 Report of a systematic review of Mersenne numbers 2^p-1 for p ...
Holmes, S. M. +7 more
core
On generalized Mersenne numbers, their interpretations and matrix generators
, 2018 In this paper we introduce generalized Mersenne numbers. We shall present some of their interpretations and matrix generators which are very useful for determining ...
Włoch, Andrzej, Ochalik, Paweł
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A combinatorial partition of Mersenne numbers arising from spectroscopy
, 2012 An analytic proof has been developed for a conjecture postulating a finite and non-integer, though rational, partitioning of Mersenne numbers, i.e., those of form 2n−1.
Eakin, R.T.
core +1 more source
MathematicsIn this paper, using the symmetrizing operator δe1e22−l, we derive new generating functions of the products of p,q-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas ...
Ali Boussayoud +2 more
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, 2022 Motivated by recently developed interest to the distribution of $q$-arydigits of Mersenne numbers $M_p = 2^p-1$, where $p$ is prime, we estimaterational exponential sums with $M_p$, $p \leq X$, modulo a large power of afixed odd prime $q$. In turn this immediately implies the normality of stringsof $q$-ary digits amongst about $(\log X)^{3/2+o(1 ...
Kerr, B. ; https://orcid.org/0000-0002-8829-372X +2 more
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