Abstract
A subset of the integers larger than 1 is primitive if no member divides another. Erdős proved in 1935 that the sum of 1 / ( a log a ) 1/(a\log a) for a a running over a primitive set A A is universally bounded over all choices for A A . In 1988 he asked if this universal bound is attained for the set of prime numbers. In this paper we make some progress on several fronts and show a connection to certain prime number “races” such as the race between π ( x ) \pi (x) and l i ( x ) \mathrm {li}(x) .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the American Mathematical Society, Series B
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
