A. Kourbatov

activity

20132020

most citedMaximal gaps between prime k-tuples: a statistical approach

7 citations · 30 across the 11 of their papers we have counts for

collaborators

11 papers

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★ 5 cited

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.NT2017★ 3 cited

On the nth record gap between primes in an arithmetic progression

Alexei Kourbatov

Let $q > r \geq 1$ be coprime integers. Let $R (n, q, r)$ be the $n$ th record gap between primes in the arithmetic progression $r$ , $r + q$ , $r + 2 q, \dots,$ and denote by $N_{q, r} (x)$ the num…

math.NT2016★ 2 cited

On the distribution of maximal gaps between primes in residue classes

Alexei Kourbatov

Let $q > r \geq 1$ be coprime positive integers. We empirically study the maximal gaps $G_{q, r} (x)$ between primes $p = q n + r \leq x$ , $n \in N$ . Extensive computations suggest that…

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…

math.NT2015★ 1 cited

Upper bounds for prime gaps related to Firoozbakht's conjecture

Alexei Kourbatov

We study two kinds of conjectural bounds for the prime gap after the k-th prime $p_{k}$ : (A) $p_{k + 1} < (p_{k})^{1 + 1/ k}$ and (B) $p_{k + 1} - p_{k} < lo g^{2} p_{k} - lo g p_{k} - b$ for $k > 9$ . Th…

math.NT2015★ 7 cited

Verification of the Firoozbakht conjecture for primes up to four quintillion

Alexei Kourbatov

If $p_{k}$ is the k-th prime, the Firoozbakht conjecture states that the sequence $(p_{k})^{1/ k}$ is strictly decreasing. We use the table of first-occurrence prime gaps in combination…

math.AP2015

Lyapunov Exponents for Burgers' Equation

Alexei Kourbatov

We establish the existence, uniqueness, and stability of the stationary solution of the one-dimensional viscous Burgers equation with the Dirichlet boundary conditions on a finite…

math.NT2014★ 5 cited

The distribution of maximal prime gaps in Cramer's probabilistic model of primes

Alexei Kourbatov

In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribut…

math.NT2013

Tables of record gaps between prime constellations

Alexei Kourbatov

We present tables of record (maximal) gaps between densest prime constellations, or k-tuplets. The tables contain all maximal gaps between prime k-tuplets up to 10^15, for each k<=…

math.NT2013★ 7 cited

Maximal gaps between prime k-tuples: a statistical approach

Alexei Kourbatov

Combining the Hardy-Littlewood k-tuple conjecture with a heuristic application of extreme-value statistics, we propose a family of estimator formulas for predicting maximal gaps be…