Computing Prime Harmonic Sums

Eric Bach; Dominic Klyve; Jonathan P Sorenson

doi:10.1090/S0025-5718-09-02249-2

Computing Prime Harmonic Sums

Eric Bach, Dominic Klyve, Jonathan P Sorenson

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.

Original language	American English
Journal	Scholarship and Professional Work - LAS
Volume	78
DOIs	https://doi.org/10.1090/S0025-5718-09-02249-2
State	Published - Jan 1 2009

Keywords

Meissel-Lehmer
algorithm
prime harmonic sum

Disciplines

Applied Mathematics
Computer Sciences

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Computing Prime Harmonic SumsFinal published version, 289 KBLicense: Unspecified

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title = "Computing Prime Harmonic Sums",

abstract = " We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.",

keywords = "Meissel-Lehmer, algorithm, prime harmonic sum",

author = "Eric Bach and Dominic Klyve and Sorenson, \{Jonathan P\}",

note = "E. Bach, D. Klyve, and J. Sorenson, Computing Prime Harmonic Sums, Mathematics of Computation 78:2283-2305, 2009.",

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AU - Bach, Eric

AU - Klyve, Dominic

AU - Sorenson, Jonathan P

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PY - 2009/1/1

Y1 - 2009/1/1

N2 - We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.

AB - We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.

KW - Meissel-Lehmer

KW - algorithm

KW - prime harmonic sum

UR - https://digitalcommons.butler.edu/facsch_papers/98

U2 - 10.1090/S0025-5718-09-02249-2

DO - 10.1090/S0025-5718-09-02249-2

M3 - Article

VL - 78

JO - Scholarship and Professional Work - LAS

JF - Scholarship and Professional Work - LAS

ER -

Computing Prime Harmonic Sums

Abstract

Keywords

Disciplines

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