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Entropy, Periodicity and the Probability of Primality [PDF]
EntropyThe distribution of prime numbers has long been viewed as a balance between order and randomness. In this work, we investigate the relationship between entropy, periodicity, and primality through the computational framework of the binary derivative.
Grenville J. Croll
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A primality test for Kpⁿ⁺¹ numbers and a generalization of Safe primes and Sophie Germain primes [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we provide a generalization of Proth's theorem for integers of the form Kpⁿ⁺¹. In particular, a primality test that requires a modular exponentiation (with a proper base a) similar to that of Fermat's test without the computation of any ...
Abdelrahman Ramzy
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On the calculation of integer sequences, associated with twin primes
Lietuvos Matematikos Rinkinys, 2023 The twin primes conjecture states that there are infinitely many twin primes. While studying this hypothesis, many important results were obtained, but the problem remains unsolved.
Igoris Belovas +2 more
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A Remark on the Factorization of Factorials [PDF]
Mathematics Interdisciplinary Research, 2021 The subject of this paper is to study distribution of the prime factors p and their exponents, which we denote by vp (n!), in standard factorization of n! into primes. We show that for each θ > 0 the primes p not exceeding nθ eventually assume almost all
Mehdi Hassani, Mahmoud Marie
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The Prime state and its quantum relatives [PDF]
Quantum, 2020 The Prime state of $n$ qubits, ${|\mathbb{P}_n{\rangle}}$, is defined as the uniform superposition of all the computational-basis states corresponding to prime numbers smaller than $2^n$. This state encodes, quantum mechanically, arithmetic properties of
D. García-Martín +4 more
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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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On the distribution of twin primes [PDF]
International Journal of Contemporary Mathematical Sciences, 2021 10 ...
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On the Distribution of Atkin and Elkies Primes [PDF]
Foundations of Computational Mathematics, 2014 17 pages, minor ...
Igor E. Shparlinski +1 more
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An Analytic Approximation to the Density of Twin Primes
Recoletos Multidisciplinary Research Journal, 2018 The highly irregular and rough fluctuations of the twin primes below or equal to a positive integer x are considered in this study. The occurrence of a twin prime on an interval [0,x] is assumed to be random.
Dionisel Y. Regalado, Rodel Azura
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The Sampling Distribution of Primes [PDF]
Proceedings of the National Academy of Sciences, 1963 This paper was communicated to the journal by H. S. Vandiver, number theorist and fellow of the US National Academy of Sciences.
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