InforLorV4, Main, Exploration, bibRecord, 00B342

New experimental results concerning the Goldbach conjecture

Identifieur interne : 00B342 ( Main/Exploration ); précédent : 00B341; suivant : 00B343

New experimental results concerning the Goldbach conjecture

Auteurs : J. M. Deshouillers [France] ; H. J. J. Te Riele [Pays-Bas] ; Y. Saouter [France]

Source :

Lecture Notes in Computer Science [ 0302-9743 ]

RBID : ISTEX:36BC123332A90C5929A3EC9C6AD7061EFE6E7AC8

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.

Url:

https://api.istex.fr/ark:/67375/HCB-T44DGBVT-4/fulltext.pdf

DOI: 10.1007/BFb0054863

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Istex, to step Corpus: 000C90
to stream Istex, to step Curation: 000C82
to stream Istex, to step Checkpoint: 002574
to stream Main, to step Merge: 00BA64
to stream Main, to step Curation: 00B342

Le document en format XML

<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">New experimental results concerning the Goldbach conjecture</title>
<author><name sortKey="Deshouillers, J M" sort="Deshouillers, J M" uniqKey="Deshouillers J" first="J. M." last="Deshouillers">J. M. Deshouillers</name>
</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>
</author>
<author><name sortKey="Saouter, Y" sort="Saouter, Y" uniqKey="Saouter Y" first="Y." last="Saouter">Y. Saouter</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:36BC123332A90C5929A3EC9C6AD7061EFE6E7AC8</idno>
<date when="1998" year="1998">1998</date>
<idno type="doi">10.1007/BFb0054863</idno>
<idno type="url">https://api.istex.fr/ark:/67375/HCB-T44DGBVT-4/fulltext.pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000C90</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000C90</idno>
<idno type="wicri:Area/Istex/Curation">000C82</idno>
<idno type="wicri:Area/Istex/Checkpoint">002574</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">002574</idno>
<idno type="wicri:doubleKey">0302-9743:1998:Deshouillers J:new:experimental:results</idno>
<idno type="wicri:Area/Main/Merge">00BA64</idno>
<idno type="wicri:Area/Main/Curation">00B342</idno>
<idno type="wicri:Area/Main/Exploration">00B342</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">New experimental results concerning the Goldbach conjecture</title>
<author><name sortKey="Deshouillers, J M" sort="Deshouillers, J M" uniqKey="Deshouillers J" first="J. M." last="Deshouillers">J. M. Deshouillers</name>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>Mathématiques Stochastiques, Université Victor Segalen Bordeaux 2, F-33076, Bordeaux Cedex</wicri:regionArea>
<placeName><region type="region" nuts="2">Nouvelle-Aquitaine</region>
<region type="old region" nuts="2">Aquitaine</region>
<settlement type="city">Bordeaux</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</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 wicri:level="1"><country xml:lang="fr">Pays-Bas</country>
<wicri:regionArea>Centre for Mathematics and Computer Science, CWI, Kruislaan 413, 1098, SJ Amsterdam</wicri:regionArea>
<wicri:noRegion>SJ Amsterdam</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Pays-Bas</country>
</affiliation>
</author>
<author><name sortKey="Saouter, Y" sort="Saouter, Y" uniqKey="Saouter Y" first="Y." last="Saouter">Y. Saouter</name>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>Institut de Recherche en Informatique de Toulouse, 118 route de Narbonne, F-31062, Toulouse Cedex</wicri:regionArea>
<placeName><region type="region" nuts="2">Occitanie (région administrative)</region>
<region type="old region" nuts="2">Midi-Pyrénées</region>
<settlement type="city">Toulouse</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</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>
<affiliations><list><country><li>France</li>
<li>Pays-Bas</li>
</country>
<region><li>Aquitaine</li>
<li>Midi-Pyrénées</li>
<li>Nouvelle-Aquitaine</li>
<li>Occitanie (région administrative)</li>
</region>
<settlement><li>Bordeaux</li>
<li>Toulouse</li>
</settlement>
</list>
<tree><country name="France"><region name="Nouvelle-Aquitaine"><name sortKey="Deshouillers, J M" sort="Deshouillers, J M" uniqKey="Deshouillers J" first="J. M." last="Deshouillers">J. M. Deshouillers</name>
</region>
<name sortKey="Deshouillers, J M" sort="Deshouillers, J M" uniqKey="Deshouillers J" first="J. M." last="Deshouillers">J. M. Deshouillers</name>
<name sortKey="Saouter, Y" sort="Saouter, Y" uniqKey="Saouter Y" first="Y." last="Saouter">Y. Saouter</name>
<name sortKey="Saouter, Y" sort="Saouter, Y" uniqKey="Saouter Y" first="Y." last="Saouter">Y. Saouter</name>
</country>
<country name="Pays-Bas"><noRegion><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>
</noRegion>
<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>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 00B342 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 00B342 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     ISTEX:36BC123332A90C5929A3EC9C6AD7061EFE6E7AC8
   |texte=   New experimental results concerning the Goldbach conjecture
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur la recherche en informatique en Lorraine

New experimental results concerning the Goldbach conjecture

New experimental results concerning the Goldbach conjecture

Source :

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri