{"id":"https://openalex.org/W2038918688","doi":"https://doi.org/10.1090/s0025-5718-97-00875-2","title":"Seven consecutive primes in arithmetic progression","display_name":"Seven consecutive primes in arithmetic progression","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2038918688","doi":"https://doi.org/10.1090/s0025-5718-97-00875-2","mag":"2038918688"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-97-00875-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00875-2","pdf_url":"https://www.ams.org/mcom/1997-66-220/S0025-5718-97-00875-2/S0025-5718-97-00875-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1997-66-220/S0025-5718-97-00875-2/S0025-5718-97-00875-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032979251","display_name":"Harvey Dubner","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Harvey Dubner","raw_affiliation_strings":["449 Beverly Road, Ridgewood, New Jersey 07450"],"affiliations":[{"raw_affiliation_string":"449 Beverly Road, Ridgewood, New Jersey 07450","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106628035","display_name":"Harry N. Nelson","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138311","display_name":"Lawrence Livermore National Security","ror":"https://ror.org/03z21mf61","country_code":"US","type":"government","lineage":["https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harry Nelson","raw_affiliation_strings":["4259 Erory Way, Livermore, California 94550"],"affiliations":[{"raw_affiliation_string":"4259 Erory Way, Livermore, California 94550","institution_ids":["https://openalex.org/I4210138311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032979251"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7053,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66087388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"66","issue":"220","first_page":"1743","last_page":"1749"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.9108390808105469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8415936231613159},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.7543778419494629},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5196986794471741},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4753444194793701},{"id":"https://openalex.org/keywords/geometric-progression","display_name":"Geometric progression","score":0.46997135877609253},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4366753101348877},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.41165611147880554},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3216252028942108},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2788534164428711},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0865854024887085}],"concepts":[{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.9108390808105469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8415936231613159},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7543778419494629},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5196986794471741},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4753444194793701},{"id":"https://openalex.org/C14367171","wikidata":"https://www.wikidata.org/wiki/Q173523","display_name":"Geometric progression","level":2,"score":0.46997135877609253},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4366753101348877},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.41165611147880554},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3216252028942108},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2788534164428711},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0865854024887085},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-97-00875-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00875-2","pdf_url":"https://www.ams.org/mcom/1997-66-220/S0025-5718-97-00875-2/S0025-5718-97-00875-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.7165","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.7165","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1997-66-220/S0025-5718-97-00875-2/S0025-5718-97-00875-2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-97-00875-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00875-2","pdf_url":"https://www.ams.org/mcom/1997-66-220/S0025-5718-97-00875-2/S0025-5718-97-00875-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2038918688.pdf","grobid_xml":"https://content.openalex.org/works/W2038918688.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1555475515","https://openalex.org/W1585160083","https://openalex.org/W1974129186","https://openalex.org/W1977864917","https://openalex.org/W2005088916","https://openalex.org/W2047359249","https://openalex.org/W2111158824","https://openalex.org/W3145898342","https://openalex.org/W3175367423","https://openalex.org/W4212875219","https://openalex.org/W4230256952","https://openalex.org/W6722663125","https://openalex.org/W6812011559"],"related_works":["https://openalex.org/W4226173127","https://openalex.org/W3013063768","https://openalex.org/W1868338274","https://openalex.org/W54883966","https://openalex.org/W2096450961","https://openalex.org/W2348231333","https://openalex.org/W2797494268","https://openalex.org/W2605523723","https://openalex.org/W1858811959","https://openalex.org/W2949823170"],"abstract_inverted_index":{"It":[0],"is":[1,38,42],"conjectured":[2],"that":[3,44],"there":[4],"exist":[5],"arbitrarily":[6],"long":[7],"sequences":[8],"of":[9,21,48,76],"<italic>consecutive</italic>":[10],"primes":[11,24,34,79],"in":[12,25,35,80],"arithmetic":[13,26,36,81],"progression.":[14,82],"In":[15],"1967,":[16],"the":[17,54,65,72],"first":[18,55],"such":[19],"sequence":[20],"6":[22],"consecutive":[23,33,78],"progression":[27,37],"was":[28],"found.":[29],"Searching":[30],"for":[31],"7":[32,77],"difficult":[39],"because":[40],"it":[41],"necessary":[43],"a":[45],"prescribed":[46],"set":[47],"at":[49],"least":[50],"1254":[51],"numbers":[52],"between":[53],"and":[56,68,70],"last":[57],"prime":[58],"all":[59],"be":[60],"composite.":[61],"This":[62],"article":[63],"describes":[64],"search":[66],"theory":[67],"methods,":[69],"lists":[71],"only":[73],"known":[74],"example":[75]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}