Zhi-Wei Sun
Published 2012-09-17, updated 2012-09-19Version 3
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.
Comments: 6 pages. Make Theorem 1.2 general
Equidistribution and inequalities for partitions into powers
Inequalities involving the primorial counting function
Two inequalities on the areal Mahler measure
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