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Mathematics of Computation

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An upper bound on Jacobsthal's function


Authors: Fintan Costello and Paul Watts
Journal: Math. Comp. 84 (2015), 1389-1399
MSC (2010): Primary 11N25; Secondary 11Y55
DOI: https://doi.org/10.1090/S0025-5718-2014-02896-2
Published electronically: November 6, 2014
MathSciNet review: 3315513
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Abstract: The function $ h(k)$ represents the smallest number $ m$ such that every sequence of $ m$ consecutive integers contains an integer coprime to the first $ k$ primes. We give a new computational method for calculating strong upper bounds on $ h(k)$.


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Additional Information

Fintan Costello
Affiliation: School of Computer Science and Informatics, University College Dublin, Belfield, Dublin 6, Ireland
Email: fintan.costello@ucd.ie

Paul Watts
Affiliation: Department of Mathematical Physics, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland
Email: watts@thphys.nuim.ie

DOI: https://doi.org/10.1090/S0025-5718-2014-02896-2
Received by editor(s): May 24, 2012
Received by editor(s) in revised form: September 16, 2013, and September 26, 2013
Published electronically: November 6, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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