Results 21 to 30 of about 10,503 (288)
Predicting Maximal Gaps in Sets of Primes
Mathematics, 2019 Let q > r ≥ 1 be coprime integers. Let P c = P c ( q , r , H ) be an increasing sequence of primes p satisfying two conditions: (i) p ≡ r (mod q) and (ii) p starts a prime k-tuple with a given pattern H ...
Alexei Kourbatov, Marek Wolf
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Figurate primes and Hilbert's 8th problem
, 2014 In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem, including Goldbach'
Cai, Tianxin +2 more
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Catalan numbers, primes, and twin primes
Elemente der Mathematik, 2008 Dieser Artikel beabsichtigt, einige Beziehungen zwischen Catalan-Zahlen, Primzahlen und Primzahlzwillingen darzustellen, indem nur elementare arithmetische Begriffe angewendet, gleichzeitig aber auch viele (historische) Bezuge fur den an einer weiteren Ausfuhrung interessierten Leser angeboten werden.
Aebi, Christian., Cairns, Grant.
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Journal of Number Theory, 1993 Let \(c\) be a positive constant, and let \(N_ c (x)\) denote the number of primes \(p \leq x\) for which \([p^ c]\) is also prime. \textit{A. Balog} [Publ. Math. Orsay 89/01, 3-11 (1989; Zbl 0712.11056)] proved that \[ N_ c(x) \sim c^{-1} x(\log x)^{-2} \] for \(c < 5/6\), and that \(\limsup_{x \to \infty} {N_ c(x) \over c^{-1} x(\log x)^{-2}} \geq 1\)
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, 2017 Currently there is no known efficient formula for primes. Besides that, prime numbers have great importance in e.g., information technology such as public-key cryptography, and their position and possible or impossible functional generation among the ...
Kristyan, Sandor
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Purpose Cognitive and psychological difficulties could negatively interfere with treatment adherence and quality of life before and after hematopoietic stem cell transplant (HSCT). Methods to mitigate these changes may have positive effects on treatment success.
Kristen L. Votruba +11 more
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Some Properties and Algorithms for Twin Primes
Applied SciencesIn this article, we study some new properties of twin primes and algorithms for their generation. We find the necessary conditions to generate a pair of twins.
Gerardo Iovane +3 more
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Prime Harmonics and Twin Prime Distribution [PDF]
, 2020 Distribution of twin primes is a long standing problem in the number theory. As of present, it is not known if the set of twin primes is finite, the problem known as twin prime conjecture. An analysis of prime modulo cycles, or prime harmonics in this work allowed to define approaches in estimation of twin prime distributions with good accuracy of ...
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Crosstalk between the ribosome quality control‐associated E3 ubiquitin ligases LTN1 and RNF10
FEBS Letters, EarlyView.Loss of the E3 ligase LTN1, the ubiquitin‐like modifier UFM1, or the deubiquitinating enzyme UFSP2 disrupts endoplasmic reticulum–ribosome quality control (ER‐RQC), a pathway that removes stalled ribosomes and faulty proteins. This disruption may trigger a compensatory response to ER‐RQC defects, including increased expression of the E3 ligase RNF10 ...
Yuxi Huang +8 more
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Polignac Numbers, Conjectures of Erd\"os on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture [PDF]
, 2013 In the present work we prove a number of surprising results about gaps between consecutive primes and arithmetic progressions in the sequence of generalized twin primes which could not have been proven without the recent fantastic achievement of Yitang ...
Pintz, Janos
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