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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


 English version:
Proceedings of the Steklov Institute of Mathematics, 2021, 314, 144–202

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