A space-efficient fast prime number sieve

We present a new algorithm that finds all primes up to n using at most O( n log log n ) arithmetic operations and O( n (log n log log n) ) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime nu...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Information processing letters Ročník 59; číslo 2; s. 79 - 84
Hlavní autoři: Dunten, Brian, Jones, Julie, Sorenson, Jonathan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 22.07.1996
Elsevier Science
Elsevier Sequoia S.A
Témata:
Algebra
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis of algorithms
Applied sciences
Computer science; control theory; systems
Design of algorithms
Exact sciences and technology
Information processing
Mathematical analysis
Mathematics
Number theoretic algorithms
Number theory
Prime number sieve
Prime numbers
Sciences and techniques of general use
Sieve of Eratosthenes
Studies
Theoretical computing
Design of algorithms
Analysis of algorithms
Prime number sieve
Sieve of Eratosthenes
Number theoretic algorithms
Algorithms
Arithmetic operation
Eratosthène sieve
Algorithm analysis
Prime number
ISSN:0020-0190, 1872-6119
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We present a new algorithm that finds all primes up to n using at most O( n log log n ) arithmetic operations and O( n (log n log log n) ) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of Θ ( log n). In addition, we present the results of our implementations of most known prime number sieves.
AbstractList We present a new algorithm that finds all primes up to n using at most O( n log log n ) arithmetic operations and O( n (log n log log n) ) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard. Our new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of Θ ( log n). In addition, we present the results of our implementations of most known prime number sieves.
A prime number sieve is an algorithm that constructs a list of primes up to a given bound n. A new algorithm is presented that finds all primes up to n using at most O(n/log log n) arithmetic operations and O(n/(log n log log n)) space. This algorithm is an improvement of a linear prime number sieve due to Pritchard (1981). The new algorithm matches the running time of the best previous prime number sieve, but uses less space by a factor of theta (log n). In addition, the results of the implementations of most known prime number sieves are presented.
Author Jones, Julie
Dunten, Brian
Sorenson, Jonathan
Author_xml – sequence: 1
  givenname: Brian
  surname: Dunten
  fullname: Dunten, Brian
– sequence: 2
  givenname: Julie
  surname: Jones
  fullname: Jones, Julie
– sequence: 3
  givenname: Jonathan
  surname: Sorenson
  fullname: Sorenson, Jonathan
  email: sorenson@butler.edu
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3194368$$DView record in Pascal Francis
BookMark eNqFkE1LAzEQhoNUsK3-Aw-LeLCH1Umym2w8CKX4BQUveg7Z7ARS2t2apAX_vbu0ePCgp2Hged8ZngkZtV2LhFxSuKVAxR0AgxyoghslZgCgVM5PyJhWkuWCUjUi4x_kjExiXPWQKLgck9k8i1tjMUfnvPXYpsyZmLJt8BvM2t2mxpBFj3s8J6fOrCNeHOeUfDw9vi9e8uXb8-tivswtF5Byp1RTWIUFd1ZRVhWNaiSDCmpWGkQrZS0FNqVhDaPSlIIrNKKGUqDkpXF8Sq4OvdvQfe4wJr3qdqHtT2rGJZMSVNlD10fIRGvWLpjW-qiHr0340pyqgouqx4oDZkMXY0D3Q1DQgzo9eNGDF62GpVeneR-7_xWzPpnkuzYF49f_hR8OYewl7T0GHQevFhsf0CbddP7vgm8M8Ia7
CODEN IFPLAT
CitedBy_id crossref_primary_10_1145_2957759
crossref_primary_10_1090_S0025_5718_2013_02787_1
crossref_primary_10_3390_a17040157
crossref_primary_10_3390_sym14122527
Cites_doi 10.1145/359657.359660
10.1007/BF00264164
10.1007/BF00289493
10.1016/0196-6774(83)90014-7
10.1145/358527.358540
10.1006/jagm.1994.1006
10.1016/0004-3702(79)90013-4
10.1007/BF01932283
10.1006/inco.1994.1082
10.1016/0167-6423(87)90024-4
ContentType Journal Article
Copyright 1996
1996 INIST-CNRS
Copyright Elsevier Sequoia S.A. Jul 22, 1996
Copyright_xml – notice: 1996
– notice: 1996 INIST-CNRS
– notice: Copyright Elsevier Sequoia S.A. Jul 22, 1996
DBID AAYXX
CITATION
IQODW
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1016/0020-0190(96)00099-3
DatabaseName CrossRef
Pascal-Francis
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
Applied Sciences
Mathematics
EISSN 1872-6119
EndPage 84
ExternalDocumentID 10210144
3194368
10_1016_0020_0190_96_00099_3
0020019096000993
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
29I
4.4
457
4G.
5GY
5VS
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABBOA
ABEFU
ABFNM
ABFSI
ABJNI
ABMAC
ABTAH
ABXDB
ABYKQ
ACDAQ
ACGFS
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADJOM
ADMUD
AEBSH
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BKOMP
BLXMC
CS3
DU5
E.L
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HLZ
HMJ
HVGLF
HZ~
IHE
J1W
KOM
LG9
M26
M41
MO0
MS~
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
PQQKQ
Q38
R2-
RIG
ROL
RPZ
SBC
SDF
SDG
SDP
SES
SEW
SME
SPC
SPCBC
SSV
SSZ
T5K
TN5
UQL
WH7
WUQ
XPP
ZMT
ZY4
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
AFXIZ
AGCQF
AGRNS
BNPGV
IQODW
SSH
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c360t-f99d4c9e43fc91284d9d72080b25aeec77b76ed5a2d217a5639ea6b056e735af3
ISICitedReferencesCount 8
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=0020019096000993&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0020-0190
IngestDate Fri Jul 25 03:50:48 EDT 2025
Mon Jul 21 09:15:39 EDT 2025
Sat Nov 29 02:29:44 EST 2025
Tue Nov 18 21:57:41 EST 2025
Fri Feb 23 02:33:11 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Design of algorithms
Analysis of algorithms
Prime number sieve
Sieve of Eratosthenes
Number theoretic algorithms
Algorithms
Arithmetic operation
Eratosthène sieve
Algorithm analysis
Prime number
Language English
License https://www.elsevier.com/tdm/userlicense/1.0
CC BY 4.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c360t-f99d4c9e43fc91284d9d72080b25aeec77b76ed5a2d217a5639ea6b056e735af3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
PQID 237277095
PQPubID 45522
PageCount 6
ParticipantIDs proquest_journals_237277095
pascalfrancis_primary_3194368
crossref_primary_10_1016_0020_0190_96_00099_3
crossref_citationtrail_10_1016_0020_0190_96_00099_3
elsevier_sciencedirect_doi_10_1016_0020_0190_96_00099_3
PublicationCentury 1900
PublicationDate 1996-07-22
PublicationDateYYYYMMDD 1996-07-22
PublicationDate_xml – month: 07
  year: 1996
  text: 1996-07-22
  day: 22
PublicationDecade 1990
PublicationPlace Amsterdam
PublicationPlace_xml – name: Amsterdam
PublicationTitle Information processing letters
PublicationYear 1996
Publisher Elsevier B.V
Elsevier Science
Elsevier Sequoia S.A
Publisher_xml – name: Elsevier B.V
– name: Elsevier Science
– name: Elsevier Sequoia S.A
References Hardy, Wright (BIB7) 1979
Bays, Hudson (BIB2) 1977; 17
Knuth (BIB8) 1981; Vol. 2
Gries, Misra (BIB6) 1978; 21
Pritchard, Pritchard (BIB9) 1981; 24
Pritchard (BIB11) 1983; 4
Pritchard (BIB13) 1994; 877
Bengelloun (BIB3) 1986; 23
Sorenson (BIB14) 1994; 16
Sorenson, Parberry (BIB15) 1994; 144
D'ooge, Robbins, Karpinski (BIB4) 1926
Pritchard (BIB12) 1987; 9
Barstow (BIB1) 1979; 12
University of Michigan Studies Humanistic Series, Vol. 16.
Pritchard (BIB10) 1982; 17
Hardy (10.1016/0020-0190(96)00099-3_BIB7) 1979
Gries (10.1016/0020-0190(96)00099-3_BIB6) 1978; 21
10.1016/0020-0190(96)00099-3_BIB5
Bays (10.1016/0020-0190(96)00099-3_BIB2) 1977; 17
Sorenson (10.1016/0020-0190(96)00099-3_BIB14) 1994; 16
Knuth (10.1016/0020-0190(96)00099-3_BIB8) 1981; Vol. 2
Sorenson (10.1016/0020-0190(96)00099-3_BIB15) 1994; 144
Pritchard (10.1016/0020-0190(96)00099-3_BIB13) 1994; 877
Pritchard (10.1016/0020-0190(96)00099-3_BIB11) 1983; 4
Bengelloun (10.1016/0020-0190(96)00099-3_BIB3) 1986; 23
Pritchard (10.1016/0020-0190(96)00099-3_BIB10) 1982; 17
Pritchard (10.1016/0020-0190(96)00099-3_BIB12) 1987; 9
Barstow (10.1016/0020-0190(96)00099-3_BIB1) 1979; 12
Pritchard (10.1016/0020-0190(96)00099-3_BIB9_2) 1981; 24
D'ooge (10.1016/0020-0190(96)00099-3_BIB4) 1926
Pritchard (10.1016/0020-0190(96)00099-3_BIB9_1) 1981; 24
References_xml – volume: 9
  start-page: 17
  year: 1987
  end-page: 35
  ident: BIB12
  article-title: Linear prime-number sieves: A family tree
  publication-title: Sci. Comput. Programming
– volume: 144
  start-page: 115
  year: 1994
  end-page: 130
  ident: BIB15
  article-title: Two fast parallel prime number sieves
  publication-title: Inform. and Comput.
– volume: 16
  start-page: 110
  year: 1994
  end-page: 144
  ident: BIB14
  article-title: Two fast GCD algorithms
  publication-title: J. Algorithms
– year: 1979
  ident: BIB7
  article-title: An Introduction to the Theory of Numbers
– volume: 877
  start-page: 280
  year: 1994
  end-page: 288
  ident: BIB13
  article-title: Improved incremental prime number sieves
  publication-title: Proc. 1st Internat. Algorithmic Number Theory Symp. (ANTS-1)
– volume: 21
  start-page: 999
  year: 1978
  end-page: 1003
  ident: BIB6
  article-title: A linear sieve algorithm for finding prime numbers
  publication-title: Comm. ACM
– volume: 4
  start-page: 332
  year: 1983
  end-page: 344
  ident: BIB11
  article-title: Fast compact prime number sieves (among others)
  publication-title: J. Algorithms
– volume: 23
  start-page: 119
  year: 1986
  end-page: 125
  ident: BIB3
  article-title: An incremental primal sieve
  publication-title: Acta Inform.
– reference: University of Michigan Studies Humanistic Series, Vol. 16.
– volume: Vol. 2
  year: 1981
  ident: BIB8
  publication-title: The Art of Computer Programming: Seminumerical Algorithms
– year: 1926
  ident: BIB4
  article-title: Nicomachus of Gerasa: Introduction to Arithmetic
– volume: 17
  start-page: 477
  year: 1982
  end-page: 485
  ident: BIB10
  article-title: Explaining the wheel sieve
  publication-title: Acta Inform.
– volume: 12
  start-page: 73
  year: 1979
  end-page: 119
  ident: BIB1
  article-title: An experiment in knowledge-based automatic programming
  publication-title: Artificial Intelligence
– volume: 17
  start-page: 121
  year: 1977
  end-page: 127
  ident: BIB2
  article-title: The segmented sieve of Eratosthenes and primes in arithmetic progressions to 10
  publication-title: BIT
– volume: 24
  start-page: 18
  year: 1981
  end-page: 23
  ident: BIB9
  article-title: A sublinear additive sieve for finding prime numbers
  publication-title: Comm. ACM
– volume: 21
  start-page: 999
  issue: 12
  year: 1978
  ident: 10.1016/0020-0190(96)00099-3_BIB6
  article-title: A linear sieve algorithm for finding prime numbers
  publication-title: Comm. ACM
  doi: 10.1145/359657.359660
– volume: 17
  start-page: 477
  year: 1982
  ident: 10.1016/0020-0190(96)00099-3_BIB10
  article-title: Explaining the wheel sieve
  publication-title: Acta Inform.
  doi: 10.1007/BF00264164
– volume: 877
  start-page: 280
  year: 1994
  ident: 10.1016/0020-0190(96)00099-3_BIB13
  article-title: Improved incremental prime number sieves
– ident: 10.1016/0020-0190(96)00099-3_BIB5
– volume: 23
  start-page: 119
  issue: 2
  year: 1986
  ident: 10.1016/0020-0190(96)00099-3_BIB3
  article-title: An incremental primal sieve
  publication-title: Acta Inform.
  doi: 10.1007/BF00289493
– volume: 4
  start-page: 332
  year: 1983
  ident: 10.1016/0020-0190(96)00099-3_BIB11
  article-title: Fast compact prime number sieves (among others)
  publication-title: J. Algorithms
  doi: 10.1016/0196-6774(83)90014-7
– volume: Vol. 2
  year: 1981
  ident: 10.1016/0020-0190(96)00099-3_BIB8
– year: 1926
  ident: 10.1016/0020-0190(96)00099-3_BIB4
– volume: 24
  start-page: 772
  issue: 1
  year: 1981
  ident: 10.1016/0020-0190(96)00099-3_BIB9_2
  article-title: A sublinear additive sieve for finding prime numbers
  publication-title: Comm. ACM
  doi: 10.1145/358527.358540
– year: 1979
  ident: 10.1016/0020-0190(96)00099-3_BIB7
– volume: 24
  start-page: 18
  issue: 1
  year: 1981
  ident: 10.1016/0020-0190(96)00099-3_BIB9_1
  article-title: A sublinear additive sieve for finding prime numbers
  publication-title: Comm. ACM
  doi: 10.1145/358527.358540
– volume: 16
  start-page: 110
  year: 1994
  ident: 10.1016/0020-0190(96)00099-3_BIB14
  article-title: Two fast GCD algorithms
  publication-title: J. Algorithms
  doi: 10.1006/jagm.1994.1006
– volume: 12
  start-page: 73
  year: 1979
  ident: 10.1016/0020-0190(96)00099-3_BIB1
  article-title: An experiment in knowledge-based automatic programming
  publication-title: Artificial Intelligence
  doi: 10.1016/0004-3702(79)90013-4
– volume: 17
  start-page: 121
  year: 1977
  ident: 10.1016/0020-0190(96)00099-3_BIB2
  article-title: The segmented sieve of Eratosthenes and primes in arithmetic progressions to 1012
  publication-title: BIT
  doi: 10.1007/BF01932283
– volume: 144
  start-page: 115
  issue: 1
  year: 1994
  ident: 10.1016/0020-0190(96)00099-3_BIB15
  article-title: Two fast parallel prime number sieves
  publication-title: Inform. and Comput.
  doi: 10.1006/inco.1994.1082
– volume: 9
  start-page: 17
  year: 1987
  ident: 10.1016/0020-0190(96)00099-3_BIB12
  article-title: Linear prime-number sieves: A family tree
  publication-title: Sci. Comput. Programming
  doi: 10.1016/0167-6423(87)90024-4
SSID ssj0006437
Score 1.4827262
Snippet We present a new algorithm that finds all primes up to n using at most O( n log log n ) arithmetic operations and O( n (log n log log n) ) space. This...
A prime number sieve is an algorithm that constructs a list of primes up to a given bound n. A new algorithm is presented that finds all primes up to n using...
SourceID proquest
pascalfrancis
crossref
elsevier
SourceType Aggregation Database
Index Database
Enrichment Source
Publisher
StartPage 79
SubjectTerms Algebra
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis of algorithms
Applied sciences
Computer science; control theory; systems
Design of algorithms
Exact sciences and technology
Information processing
Mathematical analysis
Mathematics
Number theoretic algorithms
Number theory
Prime number sieve
Prime numbers
Sciences and techniques of general use
Sieve of Eratosthenes
Studies
Theoretical computing
Title A space-efficient fast prime number sieve
URI https://dx.doi.org/10.1016/0020-0190(96)00099-3
https://www.proquest.com/docview/237277095
Volume 59
WOSCitedRecordID wos0020019096000993&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1872-6119
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0006437
  issn: 0020-0190
  databaseCode: AIEXJ
  dateStart: 19950113
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1La9wwEBZ5HQKlzZNu0wQfekhYRLuWbVnHpaQ0IYRAEtibkGQJFsLGrDchP7-j527SNGkOuZhdYcvG82nmG3keCH2TWgPvkAWmFWO4ULXEtaAGCyE0EOBCEuYShc_o-Xk9GrGLkK7YuXYCdDKpHx5Y-66ihjEQtk2dfYO406QwAL9B6HAEscPxvwQ_7IOSUBprVxzC1V4S3azf2jr-fd8ApN-N9f2jGKCQleTA0PrcAbuHcOOSfea95-9swLuHxAKsUr1_m2ydgHJ5O9Uxsyzu0c_3GHxYMsX54rajdTJt1vmi3gyVvMcL7qtXgr47TDSnxbOK2u8ZpHmBTTMYYI6xYjI3TvGD_BOblSIJY5CanYnbmTizf2AWTpbRak5LBrpudXhyPDpNFtp-rPShP_7uMaVyUH1PY4esOgpP8y_K8qEVHSwk4zug_GXMHUO52kAfg2uRDT0kNtGSnmyhT7FtRxa0-DY6GmZPEJJZhGQOIZlHSOYQsoOufx1f_fyNQ8cMrEj1Y4YNY02hmC6IUcwyj4Y1NAenQOal0FpRKmmlm1LkDbiiogR6qkUlgQRrSkphyC5amQBmPqPM1FTVQFZUIarCECXzgWikaYChG1ObsodIfClchXLytqvJDX9JJD2E01WtL6fyyvk0vm8eKKGnehyA9MqV-4_Ek24HNsd2XeihvSguHlZvx3MCdJ6C1_Hljc-5h9bn6-YrWplN7_Q-WlP3s3E3PQj4-wNqC46q
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+space-efficient+fast+prime+number+sieve&rft.jtitle=Information+processing+letters&rft.au=Dunten%2C+Brian&rft.au=Jones%2C+Julie&rft.au=Sorenson%2C+Jonathan&rft.date=1996-07-22&rft.issn=0020-0190&rft.volume=59&rft.issue=2&rft.spage=79&rft.epage=84&rft_id=info:doi/10.1016%2F0020-0190%2896%2900099-3&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_0020_0190_96_00099_3
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-0190&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-0190&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-0190&client=summon