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

Showing 2015Show all

3 papers · 1 filter

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…