Results 1 to 10 of about 74,960 (161)

A Scale Invariant Distribution of the Prime Numbers [PDF]

Computation, 2015
The irregular distribution of prime numbers amongst the integers has found multiple uses, from engineering applications of cryptography to quantum theory.
Wayne S. Kendal, Bent Jørgensen
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Analogs of the Prime Number Problem in a Shot Noise Suppression of the Soft-Reset Process [PDF]

Nanomaterials
The soft-reset process, or a sequence of charge emissions from a floating storage node through a transistor biased in a subthreshold bias condition, is modeled by a master (Kolmogorov–Bateman) equation.
Yutaka Hirose
doaj   +2 more sources

Entropy, Periodicity and the Probability of Primality [PDF]

Entropy
The 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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New properties of divisors of natural number [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
The divisors of a natural number are very important for several areas of mathematics, representing a promising field in number theory. This work sought to analyze new relations involving the divisors of natural numbers, extending them to prime numbers ...
Hamilton Brito da Silva
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THE DISTRIBUTION OF PRIME NUMBERS [PDF]

Nature, 2007
This is an expanded account of three lectures on the distribution of prime numbers given at the Montreal NATO school on equidistribution.
  +5 more sources

Combinatorial Models of the Distribution of Prime Numbers

Mathematics, 2021
This work is divided into two parts. In the first one, the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial ...
Vito Barbarani
doaj   +1 more source

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, E. Ribas, S. Carrazza, J.I. Latorre, G. Sierra   +4 more
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ALTERNATIVE PROOF OF THE INFINITUDE PRIMES AND PRIME PROPERTIES

Barekeng, 2023
Prime numbers is one of kind number that have many uses, one of which is cryptography. The uniqueness of prime numbers in their divisors and distributions causes prime numbers to be widely used in digital security systems. In number theory, one of famous
Dinni Rahma Oktaviani, Muhammad Habiburrohman, Fiki Syaban Nugroho   +2 more
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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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A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories

Advances in Mathematical Physics, 2021
The prime numbers have attracted mathematicians and other researchers to study their interesting qualitative properties as it opens the door to some interesting questions to be answered.
M. Abdel-Mageed, Ahmed Salim, Walid Osamy, Ahmed M. Khedr   +3 more
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