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Vinogradov’s three primes theorem with almost twin primes [PDF]
Compositio Mathematica, 2017 In this paper we prove two results concerning Vinogradov’s three primes theorem with primes that can be called almost twin primes. First, for any $m$, every sufficiently large odd integer $N$ can be written as a sum of three primes $p_{1},p_{2}$ and $p_{3}$ such that, for each $i\in \{1,2,3\}$, the interval $[p_{i},p_{i}+H]$ contains at least $m ...
Matomäki, Kaisa, Shao, Xuancheng
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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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Constellations of primes generated by twin primes [PDF]
, 2016 12 pages Addition of Corollary ...
Vladimir Shevelev, Peter J. C. Moses
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Generalized Twin Prime Formulas
, 2011 Based on Golomb's arithmetic formulas, Dirichlet series for two classes of twin primes are constructed and related to the roots of the Riemann zeta function in the critical strip.
Weber, H. J.
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Congruences characterizing twin primes
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2012 Inspired by P.A. Clement’s results in [2], we give new necessary and sufficient conditions for two prime numbers to be twin primes.
Adam Łomnicki, Jan Górowski
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Journal of Number Theory, 2023 29 pages; Revised version. Appendix with relevant Mathematica code included.
Magdaléna Tinková +2 more
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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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Largest Known Twin Primes [PDF]
Mathematics of Computation, 1990 663777 ⋅ 2 7650 ± 1 , 571305 ⋅ 2 7701 ± 1 663777 \cdot {2^{7650}} \pm 1,571305 \cdot {2^{7701}} \pm 1 and ...
B. K. Parady +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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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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