New experimental results concerning the Goldbach conjecture
Identifieur interne : 000C90 ( Istex/Corpus ); précédent : 000C89; suivant : 000C91New experimental results concerning the Goldbach conjecture
Auteurs : J. M. Deshouillers ; H. J. J. Te Riele ; Y. SaouterSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 1011. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 1014. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd number ≥7 can be written as a sum of three prime numbers, and (2) under the assumption of the Riemann hypothesis, every even positive integer can be written as a sum of at most four prime numbers. In addition, we have verified the Goldbach conjecture for all the even numbers in the intervals [105i , 105i +108], for i=3, 4,..., 20 and [1010i , 1010i + 109], for i=20,21,..., 30. A heuristic model is given which predicts the average number of steps needed to verify the Goldbach conjecture on a given interval. Our experimental results are in good agreement with this prediction. This adds to the evidence of the truth of the Goldbach conjecture.
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DOI: 10.1007/BFb0054863
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M." last="Deshouillers">J. M. Deshouillers</name><affiliation><mods:affiliation>Mathématiques Stochastiques, Université Victor Segalen Bordeaux 2, F-33076, Bordeaux Cedex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: J-H. Deshouillers@u-bordeaux2.fr</mods:affiliation></affiliation></author><author><name sortKey="Te Riele, H J J" sort="Te Riele, H J J" uniqKey="Te Riele H" first="H. J. J." last="Te Riele">H. J. J. Te Riele</name><affiliation><mods:affiliation>Centre for Mathematics and Computer Science, CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: herman@cwi.nl</mods:affiliation></affiliation></author><author><name sortKey="Saouter, Y" sort="Saouter, Y" uniqKey="Saouter Y" first="Y." last="Saouter">Y. Saouter</name><affiliation><mods:affiliation>Institut de Recherche en Informatique de Toulouse, 118 route de Narbonne, F-31062, Toulouse Cedex, France</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: Yannick.Saouter@irit.fr</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><title level="s" type="abbrev">Lect Notes Comput Sci</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 1011. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 1014. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd number ≥7 can be written as a sum of three prime numbers, and (2) under the assumption of the Riemann hypothesis, every even positive integer can be written as a sum of at most four prime numbers. In addition, we have verified the Goldbach conjecture for all the even numbers in the intervals [105i , 105i +108], for i=3, 4,..., 20 and [1010i , 1010i + 109], for i=20,21,..., 30. A heuristic model is given which predicts the average number of steps needed to verify the Goldbach conjecture on a given interval. Our experimental results are in good agreement with this prediction. This adds to the evidence of the truth of the Goldbach conjecture.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>J. -M. Deshouillers</name><affiliations><json:string>Mathématiques Stochastiques, Université Victor Segalen Bordeaux 2, F-33076, Bordeaux Cedex, France</json:string><json:string>E-mail: J-H. Deshouillers@u-bordeaux2.fr</json:string></affiliations></json:item><json:item><name>H. J. J. te Riele</name><affiliations><json:string>Centre for Mathematics and Computer Science, CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands</json:string><json:string>E-mail: herman@cwi.nl</json:string></affiliations></json:item><json:item><name>Y. Saouter</name><affiliations><json:string>Institut de Recherche en Informatique de Toulouse, 118 route de Narbonne, F-31062, Toulouse Cedex, France</json:string><json:string>E-mail: Yannick.Saouter@irit.fr</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Goldbach conjecture</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>sum of primes</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>primality test</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>vector computer</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Cray C 916</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>cluster of workstations</value></json:item></subject><arkIstex>ark:/67375/HCB-T44DGBVT-4</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>ReviewPaper</json:string></originalGenre><abstract>Abstract: The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 1011. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 1014. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd number ≥7 can be written as a sum of three prime numbers, and (2) under the assumption of the Riemann hypothesis, every even positive integer can be written as a sum of at most four prime numbers. In addition, we have verified the Goldbach conjecture for all the even numbers in the intervals [105i , 105i +108], for i=3, 4,..., 20 and [1010i , 1010i + 109], for i=20,21,..., 30. A heuristic model is given which predicts the average number of steps needed to verify the Goldbach conjecture on a given interval. Our experimental results are in good agreement with this prediction. 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Deshouillers@u-bordeaux2.fr</email><affiliation><orgName type="department">Mathématiques Stochastiques</orgName><orgName type="institution">Université Victor Segalen Bordeaux 2</orgName><address><postCode>F-33076</postCode><settlement>Bordeaux Cedex</settlement><country key="FR">FRANCE</country></address></affiliation></author><author><persName><forename type="first">H.</forename><forename type="first">J.</forename><forename type="first">J.</forename><nameLink>te</nameLink><surname>Riele</surname></persName><email>herman@cwi.nl</email><affiliation><orgName type="department">Centre for Mathematics and Computer Science</orgName><orgName type="institution">CWI</orgName><address><street>Kruislaan 413</street><postCode>1098</postCode><settlement>SJ Amsterdam</settlement><country key=""></country></address></affiliation></author><author><persName><forename type="first">Y.</forename><surname>Saouter</surname></persName><email>Yannick.Saouter@irit.fr</email><affiliation><orgName type="institution">Institut de Recherche en Informatique de Toulouse</orgName><address><street>118 route de Narbonne</street><postCode>F-31062</postCode><settlement>Toulouse Cedex</settlement><country key="FR">FRANCE</country></address></affiliation></author><idno type="istex">36BC123332A90C5929A3EC9C6AD7061EFE6E7AC8</idno><idno type="ark">ark:/67375/HCB-T44DGBVT-4</idno><idno type="DOI">10.1007/BFb0054863</idno></analytic><monogr><title level="m" type="main">Algorithmic Number Theory</title><title level="m" type="sub">Third International Symposiun, ANTS-III Portland, Oregon, USA, June 21–25, 1998 Proceedings</title><idno type="DOI">10.1007/BFb0054849</idno><idno type="book-id">3540646574</idno><idno type="ISBN">978-3-540-64657-0</idno><idno type="eISBN">978-3-540-69113-6</idno><idno type="chapter-id">Chap14</idno><editor><persName><forename type="first">Joe</forename><forename type="first">P.</forename><surname>Buhler</surname></persName></editor><imprint><biblScope unit="vol">1423</biblScope><biblScope unit="page" from="204">204</biblScope><biblScope unit="page" to="215">215</biblScope><biblScope unit="chapter-count">48</biblScope></imprint></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><title level="s" type="abbrev">Lect Notes Comput Sci</title><editor><persName><forename type="first">Gerhard</forename><surname>Goos</surname></persName></editor><editor><persName><forename type="first">Juris</forename><surname>Hartmanis</surname></persName></editor><editor><persName><forename type="first">Jan</forename><nameLink>van</nameLink><surname>Leeuwen</surname></persName></editor><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="seriesID">558</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><head>Abstract</head><p>The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 10<hi rend="superscript">11</hi>. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 10<hi rend="superscript">14</hi>. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd number ≥7 can be written as a sum of three prime numbers, and (2) under the assumption of the Riemann hypothesis, every even positive integer can be written as a sum of at most four prime numbers. In addition, we have verified the Goldbach conjecture for all the even numbers in the intervals [10<hi rend="superscript">5<hi rend="italic">i</hi></hi>, 10<hi rend="superscript">5<hi rend="italic">i</hi></hi> +10<hi rend="superscript">8</hi>], for <hi rend="italic">i</hi>=3, 4,..., 20 and [10<hi rend="superscript">10<hi rend="italic">i</hi></hi>, 10<hi rend="superscript">10<hi rend="italic">i</hi></hi> + 10<hi rend="superscript">9</hi>], for <hi rend="italic">i</hi>=20,21,..., 30.</p><p>A heuristic model is given which predicts the average number of steps needed to verify the Goldbach conjecture on a given interval. Our experimental results are in good agreement with this prediction. This adds to the evidence of the truth of the Goldbach conjecture.</p></abstract><textClass ana="keyword"><keywords xml:lang="en"><term>11P32</term><term>11Y99</term></keywords></textClass><textClass ana="keyword"><keywords xml:lang="en"><term>F.2.1</term></keywords></textClass><textClass ana="keyword"><keywords xml:lang="en"><term>Goldbach conjecture</term><term>sum of primes</term><term>primality test</term><term>vector computer</term><term>Cray <hi rend="italic">C</hi>916</term><term>cluster of workstations</term></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I17052</label><item><term type="Secondary" subtype="priority-1">Symbolic and Algebraic 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Language="En">New experimental results concerning the Goldbach conjecture</ChapterTitle><ChapterFirstPage>204</ChapterFirstPage><ChapterLastPage>215</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1998</CopyrightYear></ChapterCopyright><ChapterHistory><OnlineDate><Year>2006</Year><Month>5</Month><Day>24</Day></OnlineDate></ChapterHistory><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><BookID>3540646574</BookID><BookTitle>Algorithmic Number Theory</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>J.</GivenName><GivenName>-M.</GivenName><FamilyName>Deshouillers</FamilyName></AuthorName><Contact><Email>J-H. Deshouillers@u-bordeaux2.fr</Email></Contact></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>H.</GivenName><GivenName>J.</GivenName><GivenName>J.</GivenName><Particle>te</Particle><FamilyName>Riele</FamilyName></AuthorName><Contact><Email>herman@cwi.nl</Email></Contact></Author><Author AffiliationIDS="Aff3"><AuthorName DisplayOrder="Western"><GivenName>Y.</GivenName><FamilyName>Saouter</FamilyName></AuthorName><Contact><Email>Yannick.Saouter@irit.fr</Email></Contact></Author><Affiliation ID="Aff1"><OrgDivision>Mathématiques Stochastiques</OrgDivision><OrgName>Université Victor Segalen Bordeaux 2</OrgName><OrgAddress><Postcode>F-33076</Postcode><City>Bordeaux Cedex</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Centre for Mathematics and Computer Science</OrgDivision><OrgName>CWI</OrgName><OrgAddress><Street>Kruislaan 413</Street><Postcode>1098</Postcode><City>SJ Amsterdam</City><Country>The Netherlands</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>Institut de Recherche en Informatique de Toulouse</OrgName><OrgAddress><Street>118 route de Narbonne</Street><Postcode>F-31062</Postcode><City>Toulouse Cedex</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 10<Superscript>11</Superscript>. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 10<Superscript>14</Superscript>. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd number ≥7 can be written as a sum of three prime numbers, and (2) under the assumption of the Riemann hypothesis, every even positive integer can be written as a sum of at most four prime numbers. In addition, we have verified the Goldbach conjecture for all the even numbers in the intervals [10<Superscript>5<Emphasis Type="Italic">i</Emphasis></Superscript>, 10<Superscript>5<Emphasis Type="Italic">i</Emphasis></Superscript> +10<Superscript>8</Superscript>], for <Emphasis Type="Italic">i</Emphasis>=3, 4,..., 20 and [10<Superscript>10<Emphasis Type="Italic">i</Emphasis></Superscript>, 10<Superscript>10<Emphasis Type="Italic">i</Emphasis></Superscript> + 10<Superscript>9</Superscript>], for <Emphasis Type="Italic">i</Emphasis>=20,21,..., 30.</Para><Para>A heuristic model is given which predicts the average number of steps needed to verify the Goldbach conjecture on a given interval. Our experimental results are in good agreement with this prediction. This adds to the evidence of the truth of the Goldbach conjecture.</Para></Abstract><KeywordGroup Language="En"><Heading>1991 Mathematics Subject Classification</Heading><Keyword>11P32</Keyword><Keyword>11Y99</Keyword></KeywordGroup><KeywordGroup Language="En"><Heading>1991 Computing Reviews Classification System</Heading><Keyword>F.2.1</Keyword></KeywordGroup><KeywordGroup Language="En"><Heading>Keywords and Phrases</Heading><Keyword>Goldbach conjecture</Keyword><Keyword>sum of primes</Keyword><Keyword>primality test</Keyword><Keyword>vector computer</Keyword><Keyword>Cray <Emphasis Type="Italic">C</Emphasis>916</Keyword><Keyword>cluster of workstations</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>To appear in the Proceedings of the Algorithmic Number Theory Symposium III (Reed College, Portland, Oregon, USA, June 21–25, 1998).</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>New experimental results concerning the Goldbach conjecture</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>New experimental results concerning the Goldbach conjecture</title></titleInfo><name type="personal"><namePart type="given">J.</namePart><namePart type="given">-M.</namePart><namePart type="family">Deshouillers</namePart><affiliation>Mathématiques Stochastiques, Université Victor Segalen Bordeaux 2, F-33076, Bordeaux Cedex, France</affiliation><affiliation>E-mail: J-H. Deshouillers@u-bordeaux2.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">H.</namePart><namePart type="given">J.</namePart><namePart type="given">J.</namePart><namePart type="family">te Riele</namePart><affiliation>Centre for Mathematics and Computer Science, CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands</affiliation><affiliation>E-mail: herman@cwi.nl</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Y.</namePart><namePart type="family">Saouter</namePart><affiliation>Institut de Recherche en Informatique de Toulouse, 118 route de Narbonne, F-31062, Toulouse Cedex, France</affiliation><affiliation>E-mail: Yannick.Saouter@irit.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="ReviewPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">1998</dateIssued><copyrightDate encoding="w3cdtf">1998</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 1011. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 1014. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd number ≥7 can be written as a sum of three prime numbers, and (2) under the assumption of the Riemann hypothesis, every even positive integer can be written as a sum of at most four prime numbers. In addition, we have verified the Goldbach conjecture for all the even numbers in the intervals [105i , 105i +108], for i=3, 4,..., 20 and [1010i , 1010i + 109], for i=20,21,..., 30. A heuristic model is given which predicts the average number of steps needed to verify the Goldbach conjecture on a given interval. Our experimental results are in good agreement with this prediction. This adds to the evidence of the truth of the Goldbach conjecture.</abstract><classification displayLabel="1991 Mathematics Subject Classification">11P32</classification><classification displayLabel="1991 Mathematics Subject Classification">11Y99</classification><classification displayLabel="1991 Computing Reviews Classification System">F.2.1</classification><subject lang="en"><genre>Keywords and Phrases</genre><topic>Goldbach conjecture</topic><topic>sum of primes</topic><topic>primality test</topic><topic>vector computer</topic><topic>Cray C 916</topic><topic>cluster of workstations</topic></subject><relatedItem type="host"><titleInfo><title>Algorithmic Number Theory</title><subTitle>Third International Symposiun, ANTS-III Portland, Oregon, USA, June 21–25, 1998 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Joe</namePart><namePart type="given">P.</namePart><namePart type="family">Buhler</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1998</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I17052">Symbolic and Algebraic Manipulation</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I15033">Data Encryption</topic><topic authority="SpringerSubjectCodes" authorityURI="M14018">Algorithms</topic><topic authority="SpringerSubjectCodes" authorityURI="M25001">Number Theory</topic></subject><identifier type="DOI">10.1007/BFb0054849</identifier><identifier type="ISBN">978-3-540-64657-0</identifier><identifier type="eISBN">978-3-540-69113-6</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">55328</identifier><identifier type="BookID">3540646574</identifier><identifier type="BookChapterCount">48</identifier><identifier type="BookVolumeNumber">1423</identifier><part><date>1998</date><detail type="volume"><number>1423</number><caption>vol.</caption></detail><extent unit="pages"><start>204</start><end>215</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1998</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1998</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag, 1998</recordOrigin></recordInfo></relatedItem><identifier type="istex">36BC123332A90C5929A3EC9C6AD7061EFE6E7AC8</identifier><identifier type="ark">ark:/67375/HCB-T44DGBVT-4</identifier><identifier type="DOI">10.1007/BFb0054863</identifier><identifier type="ChapterID">14</identifier><identifier type="ChapterID">Chap14</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1998</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-RLRX46XW-4">springer</recordContentSource><recordOrigin>Springer-Verlag, 1998</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/HCB-T44DGBVT-4/record.json</uri></json:item></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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