Results 21 to 30 of about 992 (177)
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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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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Security Analysis of LNMNT-LightWeight Crypto Hash Function for IoT
IEEE Access, 2021 Conventional cryptographic techniques are inappropriate for resource-constrained applications in the Internet of Things (IoT) domain because of their high resources requirement.
Nubila Nabeel +2 more
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Human Randomness in the Rock-Paper-Scissors Game
Applied Sciences, 2022 In this study, we investigated the human capacity to generate randomness in decision-making processes using the rock-paper-scissors (RPS) game. The randomness of the time series was evaluated using the time-series data of RPS moves made by 500 subjects ...
Takahiro Komai +2 more
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IEEE Access, 2021 In this paper, we concretely formulate to derive the attacker's success probability of obtaining the shared secret keys for the Y00 protocol under a combination of a quantum collective attack with infinitely-long known-plaintext, naming it “ ...
Takehisa Iwakoshi
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Application of Statistical Shape Models to Standard Lumbar MRI for Stenosis Treatment Stratification: Severe Versus Normal Stenosis [PDF]
JOR SpineStatistical shape models (SSMs) derived from standard 2D lumbar MRIs capture coordinated morphological features that distinguish severe from normal spinal stenosis. Both intervertebral disc and combined models provide strong discriminatory power, comparable to or exceeding traditional anatomical measurements.
Foltz M +4 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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MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD [PDF]
Научно-технический вестник информационных технологий, механики и оптики, 2014 Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets ...
N. A. Balonin +2 more
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