Results 1 to 10 of about 15,692 (133)
BiEntropy, TriEntropy and Primality [PDF]
Entropy, 2020 The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes.
Grenville J. Croll
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The twin prime conjecture [PDF]
, 2014 This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory.
Motohashi, Yoichi
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Sieve methods and the twin prime conjecture
South East Asian J. of Mathematics and Mathematical Sciences, 2021 For $n \geq 3$ let $ p_n $ denote the $n^{\rm th}$ prime number. Let $[ \; ]$ denote the floor or greatest integer function. For a positive integer $m,$ let $\pi_2(m),$ denote the number of twin primes not exceeding $m.$ The twin prime conjecture states ...
Mothebe, Mbakiso Fix
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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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The Proof and Decryption of Goldbach Conjecture
Computer Sciences & Mathematics Forum, 2023 In this paper, a few mathematical bases are given firstly. Then, the step thinness τp of primes is given as τp = Lo1 = P1ΠP/(P−1) for the inner character, having an lnX logarithmic outer character. The “best estimation and mutual exchange equivalent” are
Linfu Ge
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Analyzing twin primes, Goldbach's strong conjecture and Polignac's conjecture
Annals of Mathematics and Physics, 2023 Here we analyze three well-known conjectures: (i) the existence of infinitely many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of Goldbach's strong conjecture, one must consider also the existence of an
Mercedes Orús-Lacort +2 more
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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
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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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Restriction theory of the Selberg sieve, with applications [PDF]
, 2004 The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an L^2-L^p restriction theorem for majorants of this type.
Green, Ben, Tao, Terence
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A Goldbach conjecture using twin primes [PDF]
Mathematics of Computation, 1979 The numbers 2 N = 2 ( 2 ) 1000000 2N = 2(2)1000000 are checked to determine if they can be written as the sum of two twin primes. Thirty-three numbers are found that cannot be so represented; they are all less than 5000. The largest number in the range 2 N
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