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On the set of the difference of primes


Authors: Wen Huang and XiaoSheng Wu
Journal: Proc. Amer. Math. Soc. 145 (2017), 3787-3793
MSC (2010): Primary 11N05, 37A45
DOI: https://doi.org/10.1090/proc/13533
Published electronically: April 12, 2017
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Abstract: In this work we prove that the set of the difference of primes is a $ \Delta _r^*$-set. The work is based on the recent dramatic new developments in the study of bounded gaps between primes, reached by Zhang, Maynard and Tao.


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Additional Information

Wen Huang
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, People’s Republic of China
Email: wenh@mail.ustc.edu.cn

XiaoSheng Wu
Affiliation: School of Mathematics, Hefei University of Technology, Hefei 230009, People’s Republic of China
Email: xswu@amss.ac.cn

DOI: https://doi.org/10.1090/proc/13533
Keywords: Difference of primes, $\Delta_r^*$-set, syndetic, thick set, Bohr set.
Received by editor(s): December 26, 2014
Received by editor(s) in revised form: September 17, 2015, and October 18, 2016
Published electronically: April 12, 2017
Additional Notes: The first author was supported by NSFC (11225105 and 11431012)
The second author was supported by NSFC (11401550 and 11571335). Xiosheng Wu served as corresponding author for this paper.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society

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