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Mat. Zametki, 2016, Volume 100, Issue 4, Pages 619–622 (Mi mz11109)  

Asymptotic Law of Distribution of Primes of Special Form

K. M. Eminyanab

a Financial University under the Government of the Russian Federation, Moscow
b Bauman Moscow State Technical University

Abstract: Let $\mathbb{N}_0$ be the set of natural numbers whose binary expansions have an even number of $1$'s, and let $\mathbb{N}_1=\mathbb{N} \setminus \mathbb{N}_0$. In this paper, we obtain asymptotic formulas for the number of primes $p$ not exceeding $X$ and such that $p\in \mathbb{N}_i$, $p+1\in \mathbb{N}_j$, where $i$ and $j$ take values 0 and 1 independently of each other.

Keywords: prime, binary expansion of a natural number.

DOI: https://doi.org/10.4213/mzm11109

Full text: PDF file (413 kB)
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English version:
Mathematical Notes, 2016, 100:4, 625–628

Bibliographic databases:

Received: 28.01.2016

Citation: K. M. Eminyan, “Asymptotic Law of Distribution of Primes of Special Form”, Mat. Zametki, 100:4 (2016), 619–622; Math. Notes, 100:4 (2016), 625–628

Citation in format AMSBIB
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