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JOURNALS
// Trudy Matematicheskogo Instituta imeni V.A. Steklova
// Archive
Trudy Mat. Inst. Steklova,
2021
Volume 314,
Pages
152–210
(Mi tm4163)
This article is cited in
2
papers
Consecutive Primes in Short Intervals
Artyom O. Radomskii
Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Abstract:
We obtain a lower bound for $\#\{x/2<p_n\leq x:\, p_n\equiv \dots \equiv p_{n+m}\equiv a\pmod {q}$,
$p_{n+m} - p_n\leq y\}$
, where
$p_n$
is the
$n$
th prime.
Keywords:
Euler's totient function, sieve methods, distribution of prime numbers.
UDC:
511.33
Received:
July 1, 2020
Revised:
October 28, 2020
Accepted:
November 3, 2020
DOI:
10.4213/tm4163
Fulltext:
PDF file (486 kB)
References
Cited by
English version:
Proceedings of the Steklov Institute of Mathematics, 2021,
314
,
144–202
Bibliographic databases:
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Steklov Math. Inst. of RAS
, 2025