Results 31 to 40 of about 1,699,076 (196)
On the numbers that determine the distribution of twin primes [PDF]
Surveys in Mathematics and its Applications, 2018 This paper is about a class of numbers indirectly connected to the twin primes, which have not been investigated so far. With the help of these numbers, we look at the set of twin primes from a different perspective and bring the reader's attention to ...
Antonie Dinculescu
doaj
J. Integer Seq., 2019 We define S(um)anD(ifference) numbers as ordered pairs $(m,\, m+Δ)$ such that the digital-sum $DS(m(m+Δ))=Δ.$ We consider both the decimal and the binary case. If both $m$ and $m+Δ$ are prime numbers, we refer to SanD {\em primes}. We show that the number of (decimal-based) SanD numbers less than $x$ grows as $c1\cdot x,$ where $c1 = 2/3,$ while the ...
Freeman J. Dyson +2 more
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Applications of Smarandache Function, and Prime and Coprime Functions [PDF]
, 2002 A book for people who love numbers: Smarandache Function applied to perfect numbers, congruences.
Ruiz, Sebastián Martín
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Proceedings of the American Mathematical Society, 2019 Rubinstein and Sarnak have shown, conditional on the Riemann hypothesis (RH) and the linear independence hypothesis (LI) on the nonreal zeros of ζ
Lichtman, Jared Duker +2 more
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Flat primes and thin primes [PDF]
, 2010 A number is called upper (lower) flat if its shift by +1 ( −1) is a power of 2 times a squarefree number. If the squarefree number is 1 or a single odd prime then the original number is called upper (lower) thin. Upper flat numbers which are primes arise
Broughan, Kevin A., Zhou, Qizhi
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, 2017 A prime number is a natural number that has Just two divisors: one and itself. From antiquity until our time, scientists are researching mathematical reasoning to understand the prime numbers; eminent scholars had worked on this field before it is ...
Ndiaye, Mady
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The Number of Prime Parking Functions
The Mathematical Intelligencer, 2023 A parking function of length $n$ is prime if we obtain a parking function of length $n-1$ by deleting one 1 from it. In this note we give a new direct proof that the number of prime parking functions of length $n$ is $(n-1)^{n-1}$. This proof leads to a new interpretation, in close terms to the definition of parking function.
Duarte, Rui +1 more
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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
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A note on the primality of sums [PDF]
Surveys in Mathematics and its Applications, 2022 It is shown that when adding a large number to a set of much smaller numbers, the number of primes or twin ranks (see text) in the resulted sumset can be substantially larger than the theoretical values given by the Prime Number Theorem or Hardy ...
Antonie Dinculescu
doaj
The Distribution of Prime Numbers
, 2022 In this paper, we discovered a new sequence of all prime numbers which end with a 1 or 9, the sequence defined by 𝑎(𝑛) = (𝑛^2 − 𝑛 − 1)/gcd (𝑏(𝑛), 𝑛^2 − 𝑛 − 1), with 𝑏(𝑛) satisfying the recurcive formula 𝑏(𝑛)=(𝑛 − 1). 𝑏(𝑛 − 1) − 𝑛. 𝑏(𝑛 − 2) and 𝑏(1) = 𝑏(2) = −1, the sequence 𝑎(𝑛) takes only 1’s and primes.
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