Geodesic
Asymptotic Law of Distribution of Primes of Special Form
Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 619-622

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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.
Mots-clés : prime
Keywords: binary expansion of a natural number. 
@article{MZM_2016_100_4_a12,
     author = {K. M. Eminyan},
     title = {Asymptotic {Law} of {Distribution} of {Primes} of {Special} {Form}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {619--622},
     publisher = {mathdoc},
     volume = {100},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a12/}
}
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K. M. Eminyan. Asymptotic Law of Distribution of Primes of Special Form. Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 619-622. http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a12/