Some new inequalities for primes
Number Theory
2012-09-20 v3
Abstract
For n=1,2,3,... let p_n be the n-th prime. We mainly show that p_n>n+sum_{k=1}^n p_k/k for all n>124, and sum_{k=1}^n kp_k<n^2p_n/3 for all n>30.
Cite
@article{arxiv.1209.3729,
title = {Some new inequalities for primes},
author = {Zhi-Wei Sun},
journal= {arXiv preprint arXiv:1209.3729},
year = {2012}
}
Comments
6 pages. Make Theorem 1.2 general