Number Theory

    

New Maximum Interval Between Any Number and the Nearest Prime Number and Related Conjectures

Authors: Juan Moreno Borrallo

In this short paper we prove that for n ≥ 2953652287 it exists some prime number between nand n + log(n), improving the best known proved bounds for the maximum interval between anynumber and the nearest prime number, as well as the maximum difference between two consecutiveprime numbers (prime gap). We note that this result proves some open conjectures on prime gapsand maximum intervals between any number and the nearest prime number.

Comments: 5 Pages.

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Submission history

[v1] 2023-10-25 00:17:20

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