Number Theory

    

Simple Arrangement in Which it is Possible to Arrange the Prime Numbers in Order to Obtain a Range of Occupied Consecutive Positions Greater Than Those Defined by the Legendre Conjecture

Authors: Andrea Berdondini

The Legendre conjecture tells us that there always exists a prime number between ��^2 and (�� + 1)^2. In this article, we will see that it is possible to arrange prime numbers less than or equal to N in order to obtain a consecutive number of occupied positions greater than the interval from ��^2to (�� + 1)^2. It is important to note that this result does not define a counterexample to the Legendre conjecture, but it represents an interesting theoretical result that can help us resolve many of the conjectures regarding the gap between two prime numbers

Comments: 4 Pages.

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[v1] 2024-03-25 19:47:24

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