Some new inequalities for primes

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arxiv 1209.3729 v3 pith:VUMJBCO7 submitted 2012-09-17 math.NT

Zhi-Wei Sun This is my paper

classification math.NT

keywords inequalitiesmainlyn-thprimeprimessome

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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.