Results 101 to 110 of about 524 (199)
Improving the efficiency of using multivalued logic tools. [PDF]
Sci Rep, 2023 Suleimenov IE +3 more
europepmc +1 more source
ALL EVEN (UNITARY) PERFECT POLYNOMIALS OVER F 2 WITH ONLY MERSENNE PRIMES AS ODD DIVISORS
, 2022 International audienceWe address an arithmetic problem in the ring F 2 [x]. We prove that the only (unitary) perfect polynomials over F 2 that are products of x, x + 1 and of Mersenne primes are precisely the nine (resp. nine "classes") known ones.
Rahavandrainy, Olivier +1 more
core
The influence of random number generation in dissipative particle dynamics simulations using a cryptographic hash function. [PDF]
PLoS One, 2021 Okada K, Brumby PE, Yasuoka K.
europepmc +1 more source
Mersenne Primes and the Quest to Find Them
The purpose of this thesis is to explore Mersenne primes. Mersenne primes are prime numbers of the form 2ⁿ − 1 where itself is prime. We delve into some properties of Mersenne primes and discuss conjectures about their distribution.
Levenius, Leo G.
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Artin reciprocity and Mersenne primes
, 2000 From its conception in the work of Kronecker and Hilbert until Takagi's great paper of 1920, class field theory was developed in order to prove reciprocity laws. When Artin succeeded in proving his reciprocity law in 1927, however, its role changed dramatically, and soon afterwards it became a cornerstone of class field theory.
Lenstra, H.W., Stevenhagen, P.
openaire +3 more sources
I. The Resonance Core (The Transcendental Phase) At the heart of the algorithm lies the argument of the sine function. We calculate a transcendental phase ($\theta$) defined by: $$\theta = (n \ln(n+1)) \cdot (e^2\pi)$$ • $n \ln(n+1)$: This expression
José Manuel Briceño Mendoza
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, 2009 The authors present several lemmas and theorems on Mersenne’s prime numbers. Some theorems are new. Of particular interest is the proof of primality tests on the Mersenne composite and the demonstration that the “New Mersenne Conjecture” is ...
Colonnese, Maria, Turco, Rosario
core
Shannon Entropy Loss in Mixed-Radix Conversions. [PDF]
Entropy (Basel), 2021 Vennos A, Michaels A.
europepmc +1 more source
Sieve for Mersenne prime numbers
, 2019 The algorithm generates many odd numbers, but only prime numbers of mersenne and not common prime numbers.
openaire +2 more sources