Ten Consecutive Primes In Arithmetic Progression
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Auteurs : Harvey Dubner ; Tony Forbes ; Nik Lygeros ; Michel Mizony ; Harry Nelson ; Paul Zimmermann [France]Source :
- Mathematics of Computation [ 0025-5718 ] ; 2002.
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Abstract
In 1967 the first set of 6 consecutive primes in arithmetic progression was found. In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we succeeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progression. This was made possible because of the increase in computer capability and availabiblity, and the ability to obtain computational help via the Internet. Although it is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression, it is very likely that 10 primes will remain the record for a long time.
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In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we succeeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progression. This was made possible because of the increase in computer capability and availabiblity, and the ability to obtain computational help via the Internet. Although it is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression, it is very likely that 10 primes will remain the record for a long time.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Ten Consecutive Primes In Arithmetic Progression</title><author role="aut"><persName><forename type="first">Harvey</forename><surname>Dubner</surname></persName><email></email><idno type="halauthor">132182</idno></author><author role="aut"><persName><forename type="first">Tony</forename><surname>Forbes</surname></persName><email></email><idno type="halauthor">132183</idno></author><author role="aut"><persName><forename type="first">Nik</forename><surname>Lygeros</surname></persName><email></email><idno type="halauthor">132184</idno></author><author role="aut"><persName><forename type="first">Michel</forename><surname>Mizony</surname></persName><email></email><idno type="halauthor">132185</idno></author><author role="aut"><persName><forename type="first">Harry</forename><surname>Nelson</surname></persName><email></email><idno type="halauthor">132186</idno></author><author role="aut"><persName><forename type="first">Paul</forename><surname>Zimmermann</surname></persName><email></email><idno type="idhal">paul-zimmermann</idno><idno type="halauthor">129979</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2364"></affiliation></author><editor role="depositor"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-09-26 14:53:17</date><date type="whenModified">2016-05-19 01:09:09</date><date type="whenReleased">2006-09-28 15:22:47</date><date type="whenProduced">2002</date></edition><respStmt><resp>contributor</resp><name key="108626"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00100978</idno><idno type="halUri">https://hal.inria.fr/inria-00100978</idno><idno type="halBibtex">dubner:inria-00100978</idno><idno type="halRefHtml">Mathematics of Computation, American Mathematical Society, 2002, 71 (239), pp.1323-1328</idno><idno type="halRef">Mathematics of Computation, American Mathematical Society, 2002, 71 (239), pp.1323-1328</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - 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In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we succeeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progression. This was made possible because of the increase in computer capability and availabiblity, and the ability to obtain computational help via the Internet. Although it is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression, it is very likely that 10 primes will remain the record for a long time.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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