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Well spaced integers generated by an infinite set of primes


Authors: Jeongsoo Kim and C. L. Stewart
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
Published electronically: October 8, 2014
MathSciNet review: 3293710
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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

$\displaystyle n_{i+1}-n_i>n_i/\exp ((\log n_i)^{1/2})$    

for $ i=1,2,\dots $.

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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
Email: cstewart@uwaterloo.ca

DOI: https://doi.org/10.1090/S0002-9939-2014-11979-4
Keywords: Prime factors, fractional exponential function
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.