Results 31 to 40 of about 1,598,417 (209)
Nature, 1911 I DESIRE to announce the discovery which I have made that (2181 —;1) is divisible by 43441. This leaves only 16 of the numbers (2q — 1) originally reported composite by Mersenne, still unverified. I have submitted my determination to Lt.—Col. Allan Cunningham, R.E., who has kindly verified it.
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Nature, 1912 AT various times NATURE has inserted notices of the successive discoveries in relation to Mersenne's Numbers. In the issue of August 12, 1909, Colonel Cunningham's discovery that 228479 was a factor of 2P−1 when p = 71 was announced: the other factor was 10334355636337793, but whether this was a prime or not was left undetermined.
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A Study on the Norms of Toeplitz Matrices with the Generalized Mersenne Numbers
Archives of Current Research International, 2023 In this article presents findings related to Toeplitz matrices with Mersenne numbers. We started by creating Toeplitz matrices whose components are Mersenne numbers. We then calculated the Euclidian, row and column norms of these matrices and established
Sevda Aktaş, Y. Soykan
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On the Lichtenberg hybrid quaternions [PDF]
Mathematica MoravicaIn this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
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Nature, 1895 IN 1644 the mathematician Mersenne asserted that out of the 56 primes not < 257, there were only 12 primes, viz.:—
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Fermat numbers and Mersenne numbers [PDF]
Mathematics of Computation, 1964 This paper gives details of the computations made on an IBM 7090 computer to show that the Fermat number \(F_m = 2^{2^m} +1\) is composite for \(m=14\), and that all the Mersenne numbers \(M_p=2^p-1\) \((5000 < p < 6000)\) are composite. The method used to show that the Fermat number is composite was to compute \(3^{2^n}\) modulo \(F_m\).
Selfridge, J. L., Hurwitz, Alexander
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مجلة بغداد للعلوم, 2023 In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test.
Yahia Awad, Ramiz Hindi, Haissam Chehade
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Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime greater than or equal to 11. In a previous work, starting from an M-cycle in a finite field 𝔽_ρ, it has been established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
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Computer Assisted Surgery, 2019 Purpose: Encryption of patient information has become an important issue in medical ultrasound instrumentation to secure information when images are accessed off-site.
Seung-Hyeok Shin +2 more
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The q-Integers and the Mersenne Numbers [PDF]
SSRN Electronic Journal, 2018 Here we will show that the q-integers, the q-analogue of the integers that we can find in the q-calculus, are forming an additive group having a generalized sum similar to the sum of the Tsallis q-entropies of independent systems. The symmetric form of q-integers will be studied too.
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