On a binomial coefficient and a product of prime numbers | Zendy

Horst Alzer | Zendy; József Sándor | Zendy

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On a binomial coefficient and a product of prime numbers

Author(s) -

Horst Alzer,

József Sándor

Publication year - 2011

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm110206008a

Subject(s) - mathematics , binomial coefficient , prime (order theory) , combinatorics , product (mathematics) , prime number , prime number theorem , discrete mathematics , geometry

Let Pn be the n-th prime number. We prove the following double-inequality. For all integers k≥5 we have exp[k(c0≥loglogk)]≥ k2 k/p1≥p2≥...≥pk ≥ exp[k(c1≥loglogk)] with the best possible constants c0 = 1/5 log23 + loglog5=1:10298… and c1 = 1/192log(36864/192)+loglog 192≥1/192log(p1≥p2≥…≥p192)=2.04287... This reffines a result published by Gupta and Khare in 1977.

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