A. Kourbatov

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20152020

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math.NT2020

On the first occurrences of gaps between primes in a residue class

Alexei Kourbatov, Marek Wolf

We study the first occurrences of gaps between primes in the arithmetic progression (P): $r$ , $r + q$ , $r + 2 q$ , $r + 3 q, \dots,$ where $q$ and $r$ are coprime integers, $q > r \geq 1$ . The g…

math.NT2019

Predicting maximal gaps in sets of primes

Alexei Kourbatov, Marek Wolf

Let $q > r \geq 1$ be coprime integers. Let $P_{c} = P_{c} (q, r, H)$ be an increasing sequence of primes $p$ satisfying two conditions: (i) $p \equiv r$ (mod $q$ ) and…

math.NT2016

On the geometric mean of the first n primes

Alexei Kourbatov

Let $p_{n}$ be the $n$ th prime, and consider the sequence $s_{n} = (2 \cdot 3 \dots p_{n})^{1/ n} = (p_{n} #)^{1/ n}$ , the geometric mean of the first $n$ primes. We give a short proof that $p…