A Remark on the Mandl's Inequality
Mehdi Hassani
TL;DR
This paper refines Mandl's inequality and uses it to improve bounds on the product of the first n primes, applying inequalities like AGM to establish new upper bounds.
Contribution
It introduces refined versions of Mandl's inequality and derives new bounds for the product of primes using these refinements and classical inequalities.
Findings
Refined Mandl's inequality established
New lower bounds for prime products derived
Upper bounds for prime products obtained
Abstract
In this note, first we refine Mandl's inequality. Then, we consider the product and we refine some known lower bounds for it, and we find some upper bounds for it by using Mandl's inequality and its refinement and the AGM-Inequality.
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Taxonomy
TopicsMathematical Inequalities and Applications · Point processes and geometric inequalities · Mathematics and Applications