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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.
K. Soundararajan
semanticscholar   +6 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   +2 more sources

Distribution of Square-Prime Numbers [PDF]

Missouri Journal of Mathematical Sciences, 2022
For $a \neq 1$ and $p$ prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) Numbers. For example, 75 = 3 $\cdot$ 25; 108 = 3 $\cdot$ 36; 45 = 5 $\cdot$ 9. These numbers are listed in the OEIS as A228056. We study the properties of these numbers, their distribution/density and also develop a few claims on their distribution/density.
Raghavendra Bhat
openaire   +3 more sources

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
doaj   +3 more sources

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

Chaotic Distribution of Prime Numbers and Digits of π

SSRN Electronic Journal, 2020
3 pages, 8 figures.
M. Berezowski
openaire   +3 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
doaj   +2 more sources

Distribution of the prime numbers

Bulletin of Applied Mathematics and Mathematics Education
This research explores the distribution of prime numbers, which are a fundamental topic in number theory. The study originated from the author's fascination with mathematics and the desire to discover something novel. The research proposes that the distribution of prime numbers follows a regular pattern starting from the number 2.
Lolav Ahmed Khalil
openaire   +2 more sources

An Observation on Distribution of Prime Numbers

, 2021
In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers.
D. Bahrami
openaire   +3 more sources

A conceptual proposal on the undecidability of the distribution law of prime numbers and theoretical consequences

Ratio Mathematica, 2019
Within the conceptual framework of number theory, we consider prime numbers and the classic still unsolved problem to find a complete law of their distribution.
Gianfranco Minati
doaj   +2 more sources