Number Theory

    

Attacking Legendre’s Conjecture Using Moivre-Stirling Approximation

Authors: Bijoy Rahman Arif

In this paper, we are going to prove a famous problem concerning prime numbers. Legendre’s conjecture states that there is always a prime p with n^2 < p < (n+1)^2, if n > 0. In 1912, Landau called this problem along with other three problems “unattackable at the presesnt state of mathematics.” Our approach to solve this problem is very simple. We will find a lower bound of the difference of second Chebyshev functions using a better Moiver-Stirling approximation and finally, we transfer it to the difference of first Chebyshev functions. The final difference is always greater than zero will prove Legendre’s conjecture.

Comments: 3 Pages.

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Submission history

[v1] 2016-09-09 06:28:05

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