Results 1 to 10 of about 451,554 (102)
On the Eight Levels theorem and applications towards Lucas-Lehmer primality test for Mersenne primes, I [PDF]
Arab Journal of Basic and Applied Sciences, 2023 Lucas-Lehmer test is the current standard algorithm used for testing the primality of Mersenne numbers, but it may have limitations in terms of its efficiency and accuracy.
Moustafa Ibrahim
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Minimality Conditions Equivalent to the Finitude of Fermat and Mersenne Primes [PDF]
Axioms, 2023 The question is still open as to whether there exist infinitely many Fermat primes or infinitely many composite Fermat numbers. The same question concerning Mersenne numbers is also unanswered.
Menachem Shlossberg
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BiEntropy, TriEntropy and Primality [PDF]
Entropy, 2020 The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes.
Grenville J. Croll
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Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes [PDF]
Finite Fields Their Appl., 2017 For prime powers $q$ and $q+\varepsilon$ where $\varepsilon\in\{1,2\}$, an affine resolvable design from $\mathbb{F}_q$ and Latin squares from $\mathbb{F}_{q+\varepsilon}$ yield a set of symmetric designs if $\varepsilon=2$ and a set of symmetric group ...
Hadi Kharaghani, Sho Suda
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مجلة بغداد للعلوم, 2023 In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test.
Yahia Awad, Ramiz Hindi, Haissam Chehade
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ALL EVEN (UNITARY) PERFECT POLYNOMIALS OVER F2 WITH ONLY MERSENNE PRIMES AS ODD DIVISORS [PDF]
Kragujevac Journal of MathematicsWe address an arithmetic problem in the ring F2[x]. We prove that the only (unitary) perfect polynomials over F2 that are products of x, x + 1 and of Mersenne primes are precisely the nine (resp. nine “classes”) known ones. This follows from a new result
Luis H. Gallardo, Olivier Rahavandrainy
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Software Implementation of Modular Reduction by Pseudo-mersenne Primes [PDF]
International Journal of Information Technology and Computer Science, 2023 Modern cryptosystems allow the use of operation in prime fields with special kind of modules that can speed up the prime field operation: multiplication, squaring, exponentiation.
Mariia Kovtun +3 more
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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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On the Sum of Reciprocals of Mersenne Primes
, 2017 The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where is the set
Yoshihiro Tanaka
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Some New Notes on Mersenne Primes and Perfect Numbers
, 2020 Mersenne primes are specific type of prime numbers that can be derived using the formula , where is a prime number. A perfect number is a positive integer of the form where is prime and is a Mersenne prime, and that can be written as the sum of its ...
Leomarich F. Casinillo
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