Results 51 to 60 of about 992 (177)
ON THE LARGEST PRIME FACTOR OF THE MERSENNE NUMBERS [PDF]
Bulletin of the Australian Mathematical Society, 2009 AbstractLetP(k) be the largest prime factor of the positive integerk. In this paper, we prove that the seriesis convergent for each constantα<1/2, which gives a more precise form of a result of C. L. Stewart [‘On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers’,Proc. London Math. Soc.35(3) (1977), 425–447].
Ford, Kevin +2 more
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On the fixed‐point proportion of self‐similar groups
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract We prove that super strongly fractal groups acting on regular rooted trees have null fixed‐point proportion. In particular, we show that the fixed‐point proportion of an infinite family of iterated monodromy groups of exceptional complex polynomials has the same property.
Jorge Fariña‐Asategui, Santiago Radi
wiley +1 more source
Testing Randomness Using Artificial Neural Network
IEEE Access, 2020 The vital characteristic of randomness is unpredictability. Thus any regularity will compromise the application of random numbers. Quantum random number generators (QRNGs) can provide intrinsic unpredictable randomness based on the nature of quantum ...
Yulong Feng, Lingyi Hao
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Mersenne and Fermat numbers [PDF]
Proceedings of the American Mathematical Society, 1954 The first seventeen even perfect numbers are therefore obtained by substituting these values of n in the expression 2 n-(2n -1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 21271, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime.
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Divisors of Mersenne numbers [PDF]
Mathematics of Computation, 1983 We add to the heuristic and empirical evidence for a conjecture of Gillies about the distribution of the prime divisors of Mersenne numbers. We list some large prime divisors of Mersenne numbers
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Converting Binary Floating‐Point Numbers to Shortest Decimal Strings: An Experimental Review
Software: Practice and Experience, Volume 56, Issue 4, Page 462-478, April 2026.ABSTRACT Background When sharing or logging numerical data, we must convert binary floating‐point numbers into their decimal string representations. For example, the number π might become 3.1415927. Engineers have perfected many algorithms for producing such accurate, short strings.
Jaël Champagne Gareau, Daniel Lemire
wiley +1 more source
On the intersections of nilpotent subgroups in simple groups
Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.Abstract Let G$G$ be a finite group and let Hp$H_p$ be a Sylow p$p$‐subgroup of G$G$. A recent conjecture of Lisi and Sabatini asserts the existence of an element x∈G$x \in G$ such that Hp∩Hpx$H_p \cap H_p^x$ is inclusion‐minimal in the set {Hp∩Hpg:g∈G}$\lbrace H_p \cap H_p^g \,:\, g \in G\rbrace$ for every prime p$p$.
Timothy C. Burness, Hong Yi Huang
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An Ultra-light PRNG Passing Strict Randomness Tests and Suitable for Low Cost Tags
Advances in Electrical and Computer Engineering, 2016 A pseudo-random number generator for low-cost RFID tags is presented. The scheme is simple, sequential and secure, yet has a high performance. Despite its lowest hardware complexity, our proposal represents a better alternative than previous proposals ...
OZCANHAN, M. H. +2 more
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Mathematics, 2019 In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit ...
Yunlan Wei +3 more
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On the factors of certain Mersenne numbers. II [PDF]
Mathematics of Computation, 1964 Verf. läßt einer mit \textit{G. D. Johnson} gemeinsam veröffentlichten Arbeit [Math. Comput. 14, 365--369 (1960; Zbl 0099.26305)] einen zweiten Teil folgen. Dieser verzeichnet \(899\) neue Faktoren \(q\) von \(M_p\), für \(383\le p < 20000\) und dient gleichsam als Vervollständigung früherer derartiger Verzeichnisse, etwa \textit{S.
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