2016/08/15 by Bijoy Rahman Arif, Arif, Bijoy Rahman
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1608.07240
arxiv created 2016/11/29 · arxiv updated 2016/11/30
In this paper, we are going to prove a famous problem concerning prime numbers. Bertrand postulate states that there is always a prime p with n < p < 2n, if n > 1. Bertrand postulate is not a newer one to be proven, in fact, after his assumption and numerical evidence, Chebyshev was the first person who proved it. Subsequently, Ramanujan proved it using properties of Gamma function, and Erdös published a simpler proof with the help of Primorial function, p#. Our approach is unique in the sense that we have used mathematical induction for finding the upper and lower bounds for the second Chebyshev function, and they are even stronger than Ramanujan bounds finding using Gamma function. Otherwise, our approach is similar the way Ramanujan proved it.