Results 11 to 20 of about 385 (161)
Computer Experiments with Mersenne Primes [PDF]
Computational Methods in Science and Technology, 2013 We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated geometrical means of the partial denominators of the continued fraction expansion of $\bar{\BB}_M$. We get values converging
Wolf Marek
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Efficient and Constant Time Modular Reduction With Generalized Mersenne Primes
IEEE AccessMany cryptographic applications require a vast number of modular multiplications with a large prime modulus. Generalized Mersennes are a class of primes commonly used in cryptography because of their special forms.
Serdar S. Erdem, Sezer S. Erdem
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The 25th and 26th Mersenne primes [PDF]
Mathematics of Computation, 1980 The 25th and 26th Mersenne primes are 2 21701
Noll, Curt, Nickel, Laura
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Arab Journal of Basic and Applied SciencesMersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Ibrahim
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Acerca de algunos exponentes de Mersenne (About some Mersenne exponents)
Revista Digital Matemática, Educación e InternetLos números primos de Mersenne crecen de manera vertiginosa y se vuelven intratables con las herramientas de cómputo actuales. En este trabajo se repasan brevemente las cadenas de Mersenne para mostrar cómo ese crecimiento exponencial impone un límite en
Gerardo Miramontes de León
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Mathematics of Computation, 1991 The number 2 110503
W. N. Colquitt, L. Welsh
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Public key cryptographic algorithm SM2 optimized implementation on low power embedded platform
网络与信息安全学报, 2022 With the development of wireless communication technology and the popularization of intelligent terminals, more and more cryptographic algorithms are applied to IoT devices to ensure the security of communication and data.Among them, the SM2 elliptic ...
Ganqin LIU +4 more
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Splitting Sequences for Coding and Hybrid Incremental ARQ with Fragment Retransmission
Mathematics, 2021 This paper proposes a code defined on a finite ring ℤpM, where pM = 2m−1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence (splitting set) S, defined for the given multiplier set E=±20, ±21,…, ±2m−1 ...
Dragana Bajić +2 more
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The Power of Hashing with Mersenne Primes
CoRR, 2020 The classic way of computing a $k$-universal hash function is to use a random degree-$(k-1)$ polynomial over a prime field $\mathbb Z_p$. For a fast computation of the polynomial, the prime $p$ is often chosen as a Mersenne prime $p=2^b-1$. In this paper, we show that there are other nice advantages to using Mersenne primes.
Thomas Dybdahl Ahle +2 more
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Mathematics of Computation, 1958 Am 8. September 1957 ergab die schwedische Elektronenrechenmaschine BESK (siehe auch nachstehendes Referat Zbl 0082.25602) nach einer Laufzeit von 5h 30m die Zahl \(2^{3217}-1\) als Primzahl. (Nachgeprüft am 12. September.) Sie ist, mit ihren 969 Stellen vollständig mitgeteilt, nunmehr die größe bekannte Primzahl.
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