Results 21 to 30 of about 986 (177)
Mathematics of Computation, 1958 Im Jahre 1957 prüfte der Verf. mit Hilfe der Maschine BESK die Mersenneschen Zahlen \(M_p = 2^p-1\) für \(p < 10,000\). Und zwar zunächst alle diese auf etwaige Teiler \(< 10\cdot 2^{20}\) und hierauf diejenigen für \(2300 < p < 3300\), bei denen sich kein solcher Teiler ergab, nach dem Lucas-Test auf ihre Primheit. Dabei ergab sich nur \(2^{3217}- 1\)
openaire +2 more sources
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
openaire +2 more sources
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
doaj +1 more source
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
doaj +1 more source
Nature, 1895 IN 1644 the mathematician Mersenne asserted that out of the 56 primes not < 257, there were only 12 primes, viz.:—
openaire +2 more sources
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
doaj +1 more source
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.
openaire +1 more source
Algorithms, 2023 In this paper, a hybrid nature-inspired metaheuristic algorithm based on the Genetic Algorithm and the African Buffalo Optimization is proposed. The hybrid approach adaptively switches between the Genetic Algorithm and the African Buffalo Optimization ...
Marko Gulić, Martina Žuškin
doaj +1 more source
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.
openaire +2 more sources
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
doaj