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Some new upper bounds on the generation of prime numbers

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Harry G. MairsonAuthors Info & Claims

Communications of the ACM, Volume 20, Issue 9

Pages 664 - 669

https://doi.org/10.1145/359810.359838

Published: 01 September 1977 Publication History

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Abstract

Given an integer N, what is the computational complexity of finding all the primes less than N? A modified sieve of Eratosthenes using doubly linked lists yields an algorithm of O_A(N) arithmetic complexity. This upper bound is shown to be equivalent to the theoretical lower bound for sieve methods without preprocessing. Use of preprocessing techniques involving space-time and additive-multiplicative tradeoffs reduces this upper bound to O_A(N/log logN) and the bit complexity to O_B(N logN log log logN). A storage requirement is described using O_B(N logN/log logN) bits as well.

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Ghidarcea MPopescu D(2024)Prime Time Tactics—Sieve Tweaks and BoostersAlgorithms10.3390/a1707029117:7(291)Online publication date: 3-Jul-2024
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Wang Y(2022)A Proof of the Twin Prime Conjecture in the Ƥ x Ƥ SpaceWSEAS TRANSACTIONS ON MATHEMATICS10.37394/23206.2022.21.6621(585-593)Online publication date: 25-Jul-2022
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Published In

Communications of the ACM Volume 20, Issue 9

Sept. 1977

60 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/359810

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 September 1977

Published in CACM Volume 20, Issue 9

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Ghidarcea MPopescu D(2024)Prime Number Sieving—A Systematic Review with Performance AnalysisAlgorithms10.3390/a1704015717:4(157)Online publication date: 14-Apr-2024
https://doi.org/10.3390/a17040157
Wang Y(2022)A Proof of the Twin Prime Conjecture in the Ƥ x Ƥ SpaceWSEAS TRANSACTIONS ON MATHEMATICS10.37394/23206.2022.21.6621(585-593)Online publication date: 25-Jul-2022
https://doi.org/10.37394/23206.2022.21.66
Wang Y(2022)A Proof of Goldbach Conjecture by Mirror Prime DecompositionWSEAS TRANSACTIONS ON MATHEMATICS10.37394/23206.2022.21.6321(563-571)Online publication date: 18-Jul-2022
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Bahig HHazber MAl-Utaibi KNassr DBahig H(2022)Efficient Sequential and Parallel Prime Sieve AlgorithmsSymmetry10.3390/sym1412252714:12(2527)Online publication date: 30-Nov-2022
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Paillard GFranca FLavault C(2019)A Distributed Wheel Sieve Algorithm2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)10.1109/IPDPSW.2019.00107(619-626)Online publication date: May-2019
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Bender MChowdhury RConway AFarach-Colton MGanapathi PJohnson RMcCauley SSimon BSingh S(2016)The I/O Complexity of Computing Prime TablesLATIN 2016: Theoretical Informatics10.1007/978-3-662-49529-2_15(192-206)Online publication date: 22-Mar-2016
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Kavitha T(2007)Linear time algorithms for Abelian group isomorphism and related problemsJournal of Computer and System Sciences10.1016/j.jcss.2007.03.01373:6(986-996)Online publication date: 1-Sep-2007
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Paillard GLavault CFranca F(2005)A Distributed Prime Sieving Algorithm based on Scheduling by Multiple Edge ReversalProceedings of the The 4th International Symposium on Parallel and Distributed Computing10.1109/ISPDC.2005.5(139-146)Online publication date: 4-Jul-2005
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Kavitha T(2003)Efficient Algorithms for Abelian Group Isomorphism and Related ProblemsFST TCS 2003: Foundations of Software Technology and Theoretical Computer Science10.1007/978-3-540-24597-1_24(277-288)Online publication date: 2003
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Super-linear time-space tradeoff lower bounds for randomized computation

Efficient ways of prime number generation for ring signatures

New lower bounds for halfspace emptiness

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