Some new inequalities for primes

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.

arXiv comment6 pages. Make Theorem 1.2 general

References in corpus (1)

• A Remark on the Mandl's Inequality

Cited by in corpus (1)

• New bounds for the sum of the first $n$ prime numbers