On a certain relation between Legendre's conjecture and Bertrand's postulate
Tsutomu Hashimoto
TL;DR
This paper explores a mathematical connection between Legendre's conjecture and Bertrand's postulate through a transformation of Legendre's function, revealing new properties of primes.
Contribution
It establishes a novel relation between two famous conjectures in number theory using a specific transformation of Legendre's function.
Findings
Identifies a new property of primes related to the conjectures
Shows a specific transformation links Legendre's conjecture and Bertrand's postulate
Provides a mathematical framework connecting the two conjectures
Abstract
We prove a certain relation between Legendre's conjecture and Bertrand's postulate in terms of a certain transformation of Legendre's function phi. We show a certain property of a prime.
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Taxonomy
TopicsHistory and Theory of Mathematics · Analytic Number Theory Research · Algebraic Geometry and Number Theory