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Alexei Kourbatov's Publications

**2019**

Kourbatov, A. and Wolf, M.
Predicting maximal gaps in sets of primes,
Mathematics (MDPI), 7 (2019), No.5, 400.
DOI:10.3390/math7050400,
arXiv:1901.03785.

**2018**

Kourbatov, A.
On the *n*th record gap between primes in an arithmetic progression,
International Mathematical Forum, 13 (2018), No.2, 65-78.
DOI:10.12988/imf.2018.712103,
arXiv:1709.05508.

**2016**

Kourbatov, A.
On the distribution of maximal gaps between primes in residue classes, preprint (2016). arXiv:1610.03340

Kourbatov, A.
On the geometric mean of the first *n* primes, preprint (2016). arXiv:1603.00855
(local copy)

**2015**

Kourbatov, A.
Upper bounds for prime gaps related to Firoozbakht's conjecture,
Journal of Integer Sequences, 18 (2015), Article 15.11.2, 7 pp.
MR3436186,
arXiv:1506.03042.

Kourbatov, A.
Verification of the Firoozbakht conjecture for primes up to four quintillion,
International Mathematical Forum, 10 (2015), No.6, 283-288.
DOI:10.12988/imf.2015.5322,
arXiv:1503.01744.

**2014**

Kourbatov, A.
The distribution of maximal prime gaps in Cramer's probabilistic model of primes,
International Journal of Statistics and Probability, 3 (2014), No.2, 18-29.
DOI:10.5539/ijsp.v3n2p18,
arXiv:1401.6959.

Kourbatov, A.
Is there a limiting distribution of maximal gaps between primes?
Poster presentation at the DIMACS Conference on Challenges of Identifying Integer Sequences,
October 9-10, 2014.

**2013**

Kourbatov, A.
Maximal gaps between prime k-tuples: a statistical approach,
Journal of Integer Sequences, 16 (2013), Article 13.5.2, 26 pp.
MR3065331,
arXiv:1301.2242.

Kourbatov, A.
Tables of maximal gaps between prime constellations, preprint (2013).
arXiv:1309.4053.

**2012**

Kourbatov, A.
Big Integer Calculator (Windows 8 app), available via Microsoft Windows 8 Store (2012-2016).
Please use the
online version of the Big Integer Calculator.

**1993**

Kourbatov, A.
Some estimates concerning the overlapping domain decomposition method for the convection-diffusion equation.
East-West J. Numer. Math. 1, No. 4, 303-309.
MR1318808.

**1992**

Kourbatov, A.
Lyapunov exponents for Burgers' equation (in Russian).
Prikladnaya Mekhanika i Matematika. Sbornik Nauchnykh Trudov,
Moscow Institute of Physics and Technology (1992), 96-103.
English translation:
Lyapunov exponents for Burgers' equation, arXiv:1502.06581.

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