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Testing
Published in Zaven A. Karian, Edward J. Dudewicz, Modern Statistical, Systems, and GPSS Simulation, 2020
Zaven A. Karian, Edward J. Dudewicz
The first 8 of these were claimed to be prime by Father Martin Mersenne in 1644. Thus, 231 — 1, often used as m in random number generators, is a prime number. This fact was established by Euler in 1772. The larger numbers in this list are of much more recent date. For example, the three Mersenne numbers 2e – 1 for e=521,607,1279 were established as primes at the National Bureau of Standards (now the National Institute of Standards and Technology) in 1952. There are currently 32 known Mersenne primes, the largest of which has e=756,839, and was shown to be prime in 1992 by researchers at AEA Technology’s Harwell Laboratory in Britain. This number is, in fact, the largest known prime and has 227,832 digits.
Multiplier Design Based on DBNS
Published in Vassil Dimitrov, Graham Jullien, Roberto Muscedere, Multiple-Base Number System, 2017
Vassil Dimitrov, Graham Jullien, Roberto Muscedere
The above-mentioned algorithms (Karatsuba’s, Schönhage-Strassen’s, and Fürer’s) all have a subquadratic complexity. However, the implicit constant associated with the big-O notation is very large, and this severely limits their applicability to problems of practical importance. Karatsuba’s multiplication outperforms the classical shift-and-add algorithm if the size of the multiplicands is around 1,000 bits. This makes it suitable for specific cryptographic applications. The algorithms by Schönhage-Strassen and Fürer are useful if one deals with extremely large numbers. Applications include computational number theory and computations associated with the search of large Mersenne primes and finding divisors of Fermat numbers. In those cases we deal with numbers having more than 1 million decimal digits.
Single Degree‐of‐Freedom Damped Vibration
Published in Haym Benaroya, Mark Nagurka, Seon Han, Mechanical Vibration, 2017
Haym Benaroya, Mark Nagurka, Seon Han
Euler’s identity, eiπ + 1 = 0, was called “the most remarO‐ able formula in mathematics” by Richard Feynman for its use of addition, multiplication, exponentiation, and equality,ding an dhm important constants 0, 1, e, i, and π. By 1772 Euler had proved that 231 - 1 = 2, 147, 483, 647 is a Mersenne prime. Exam have remaicO the largest Coeffi prime until 1867.
A framework on task configuration and execution for distributed geographical simulation
Published in International Journal of Digital Earth, 2021
Fengyuan Zhang, Min Chen, Ming Wang, Zihuan Wang, Shuo Zhang, Songshan Yue, Yongning Wen, Guonian Lü
Third, due to the complexity of geographical simulations, scheduling volunteers' computers and balancing the task load to enhance the running performance of geographical simulations are still challenges for scholars. For time-consuming models, users employ a collection of many computers to run models in order to save time and integrate many technologies, such as parallel running and clusters (Buyya 1999; Zaharia et al. 2010; Deng, Desjardins, and Delmelle 2019). With the development of computer technology, the number of projects for volunteered computers in other domains (biology, astronomy, chemistry, mathematics, etc.) is increasing and includes BOINC, World Community Grid, Great Internet Mersenne Prime Search (GIMPS), SETI@home, Folding@home, and Genome@Home (Anderson et al. 2002; Wanko and Venable 2002; Anderson 2004; Larson et al. 2009; Hachmann et al. 2011). These projects are forms of distributed computing that assemble volunteered computing and can support research without much funding in massive computation (Anderson 2004; Korpela 2012). This approach is suitable for simulation tasks with massive and similar computing tasks. However, geographical simulations, which involve various modes, are complex. Moreover, different graphical simulations have different model configurations. Therefore, flexible simulation configurations are necessary, and related research is lacking.
BTLA-LSDG: Blockchain-Based Triune Layered Architecture for Authenticated Subgraph Query Search in Large-Scale Dynamic Graphs
Published in IETE Journal of Research, 2023
G. Sharmila, M. K. Kavitha Devi
Initially, data owners are authenticated to the blockchain using the Four-Q-Curve algorithm, which is an asymmetric cryptography algorithm. It is better than the ECC and RSA. In this algorithm, two different keys (public and private keys) are generated for authentication. These keys are not hacked by attackers. When the data owner enters the system, then he/she must register with the blockchain. Here, the data owner ID, password, and random prime number are considered secure credentials. When these credentials are valid, then he/she is accepted to access the system. A preliminary concept of the four-q-curve is depicted in the following. Four-Q-Curve is launched by Microsoft Research in 2015, which is four to five times faster than the traditional Elliptic Curve Algorithm (NIST P-256 and Curve25519). Furthermore, ECC is old and was released in 1985 and was well known during 2004–2005. Due to its simplicity, security and speed, it is written as follows Equation (3) means that the Four-Q Curve tradeoff functionalities, where is the security, simplicity and speed, respectively. Definition 1 (Four-Q-Curve): It is a high-performance Elliptic Curve that goals to provide 128-bit security from 4Dimensional decomposition that decreases the number of processes on the elliptic curve group. where is the Edwards curve, p is the Mersenne prime number,= 125317048443780598345676279555970305165.i + 4205857648805777768770. ECC addition laws are complete on , is the 2Q curve degree of endomorphism . It is a fast arithmetic modulo prime operation i.e.. The set of Rational Points Fp2 fulfills the affine model to E forms of group. In this paper, Extended Twisted Edwards Coordinates is proposed which refers to the Affine Variables (X, Y) over . It is a projective tuple form and is represented as (x;y;z;t) Data owner-generated secret keys and session tokens are given to the Hadoop by Blockchain. When the data owner logs in to the system, then the session token is retrieved for data owners. This token is valid for a certain period of time.