Well spaced integers generated by an infinite set of primes
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- by Jeongsoo Kim and C. L. Stewart PDF
- Proc. Amer. Math. Soc. 143 (2015), 915-923 Request permission
Abstract:
In this article we prove that there exists an infinite set of prime numbers with the property that the sequence $1=n_1<n_2<\cdots$ of positive integers made up of primes from the set is well spaced. For example we prove that there is an infinite set of prime numbers for which \begin{equation*} n_{i+1}-n_i>n_i/\exp ((\log n_i)^{1/2}) \end{equation*} for $i=1,2,\dots$.References
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Additional Information
- Jeongsoo Kim
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
- C. L. Stewart
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
- MR Author ID: 167235
- Email: cstewart@uwaterloo.ca
- Received by editor(s): February 28, 2012
- Received by editor(s) in revised form: July 25, 2012
- Published electronically: October 8, 2014
- Additional Notes: The research of the second author was supported in part by the Canada Research Chairs Program and by grant A3528 from the Natural Sciences and Engineering Research Council of Canada.
- Communicated by: Matthew A. Papanikolas
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 915-923
- MSC (2010): Primary 11N25, 11J86
- DOI: https://doi.org/10.1090/S0002-9939-2014-11979-4
- MathSciNet review: 3293710