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Mathematics of Computation

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Computing $ \pi(x)$ analytically


Author: David J. Platt
Journal: Math. Comp. 84 (2015), 1521-1535
MSC (2010): Primary 11Y35; Secondary 11N37, 11N56, 11Y70
Published electronically: October 3, 2014
MathSciNet review: 3315519
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Abstract: We describe a rigorous implementation of the Lagarias and Odlyzko Analytic Method to evaluate the prime counting function and its use to compute unconditionally the number of primes less than $ 10^{24}$.


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Additional Information

David J. Platt
Affiliation: Heilbronn Institute for Mathematical Research, University of Bristol
Email: dave.platt@bris.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-2014-02884-6
Received by editor(s): March 26, 2012
Received by editor(s) in revised form: September 4, 2013
Published electronically: October 3, 2014
Additional Notes: This work formed part of the author’s Ph.D. research and he would like to thank Dr. Andrew Booker for his patient supervision. Funding was provided by the Engineering and Physical Sciences Research Council through the University of Bristol and he is grateful to both.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.