A. Kourbatov

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20152020

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Showing 2016 · math.NTShow all

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math.NT2016

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…