Abstract
Let A be any subset of positive integers, and P the set of all positive primes. Two of our results are: (a) the number of positive integers which are less than x and can be represented as 2 k + p (resp. p − 2 k ) with k ∈ A and p ∈ P is more than 0.03A(log x/ log 2)π(x) for all sufficiently large x; (b) the number of positive integers which are less than x and can be represented as 2 q + p with p, q ∈ P is (1 + o(1))π(log x/ log 2)π(x). Four related open problems and one conjecture are posed.
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 callDisclaimer: 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.
