{"id":"https://openalex.org/W2004877418","doi":"https://doi.org/10.1112/s1461157000000772","title":"Primes in Elliptic Divisibility Sequences","display_name":"Primes in Elliptic Divisibility Sequences","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2004877418","doi":"https://doi.org/10.1112/s1461157000000772","mag":"2004877418"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000000772","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000772","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E2CE61AFB56AFDBC17263F9905DED3E9/S1461157000000772a.pdf/div-class-title-primes-in-elliptic-divisibility-sequences-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E2CE61AFB56AFDBC17263F9905DED3E9/S1461157000000772a.pdf/div-class-title-primes-in-elliptic-divisibility-sequences-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009126028","display_name":"Manfred Einsiedler","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Manfred Einsiedler","raw_affiliation_strings":["Mathematical Institute, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria","Mathematical Institute, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria, Manfred.Einsiedler@univie.ac.at"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Mathematical Institute, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria, Manfred.Einsiedler@univie.ac.at","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084363747","display_name":"Graham Everest","orcid":null},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Graham Everest","raw_affiliation_strings":["School of Mathematics, University of East Anglia, Norwich NR4 7TJ","School of Mathematics, University of East Anglia, Norwich NR4 7TJ, g.everest@uea.ac.uk"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ","institution_ids":["https://openalex.org/I1118541"]},{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ, g.everest@uea.ac.uk","institution_ids":["https://openalex.org/I1118541"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050016880","display_name":"Thomas Ward","orcid":null},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thomas Ward","raw_affiliation_strings":["School of Mathematics, University of East Anglia, Norwich NR4 7TJ","School of Mathematics, University of East Anglia, Norwich NR4 7TJ, t.ward@uea.ac.uk"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ","institution_ids":["https://openalex.org/I1118541"]},{"raw_affiliation_string":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ, t.ward@uea.ac.uk","institution_ids":["https://openalex.org/I1118541"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009126028"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":5.7865,"has_fulltext":true,"cited_by_count":62,"citation_normalized_percentile":{"value":0.96296784,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9990000128746033,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/divisibility-rule","display_name":"Divisibility rule","score":0.9719085097312927},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.862262487411499},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6195009350776672},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4972896873950958},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4132183790206909},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39887329936027527},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36834001541137695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3548698425292969}],"concepts":[{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.9719085097312927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.862262487411499},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6195009350776672},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4972896873950958},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4132183790206909},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39887329936027527},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36834001541137695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3548698425292969},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1112/s1461157000000772","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000772","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E2CE61AFB56AFDBC17263F9905DED3E9/S1461157000000772a.pdf/div-class-title-primes-in-elliptic-divisibility-sequences-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dro.dur.ac.uk.OAI2:10091","is_oa":false,"landing_page_url":"http://dro.dur.ac.uk/10091/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196258","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"LMS journal of computation and mathematics, 2001, Vol.4, pp.1-13 [Peer Reviewed Journal]","raw_type":"Article"},{"id":"pmh:oai:ueaeprints.uea.ac.uk:19698","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.16.2832","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.2832","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mth.uea.ac.uk/~h720/abstracts/./eds.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.8937","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.8937","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mth.uea.ac.uk/~h090/eds.ps","raw_type":"text"},{"id":"pmh:oai:durham-repository.worktribe.com:1502489","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1502489","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1112/s1461157000000772","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000000772","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E2CE61AFB56AFDBC17263F9905DED3E9/S1461157000000772a.pdf/div-class-title-primes-in-elliptic-divisibility-sequences-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2004877418.pdf","grobid_xml":"https://content.openalex.org/works/W2004877418.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W126377560","https://openalex.org/W411273241","https://openalex.org/W1486898453","https://openalex.org/W1576086108","https://openalex.org/W1586485728","https://openalex.org/W1885434710","https://openalex.org/W1985771908","https://openalex.org/W1985860521","https://openalex.org/W2009129512","https://openalex.org/W2064005932","https://openalex.org/W2076597612","https://openalex.org/W2088573002","https://openalex.org/W2099317653","https://openalex.org/W2149910366","https://openalex.org/W2315092185","https://openalex.org/W2326135900","https://openalex.org/W2330044538","https://openalex.org/W2334368756","https://openalex.org/W2483932885","https://openalex.org/W3175367423","https://openalex.org/W4243379812","https://openalex.org/W4300182202","https://openalex.org/W6605039590","https://openalex.org/W6639454829","https://openalex.org/W6674791895","https://openalex.org/W6721644497"],"related_works":["https://openalex.org/W245125619","https://openalex.org/W1591666304","https://openalex.org/W3093741449","https://openalex.org/W2977722921","https://openalex.org/W2802582926","https://openalex.org/W3094509135","https://openalex.org/W2556813997","https://openalex.org/W2808073817","https://openalex.org/W2159790760","https://openalex.org/W2745643214"],"abstract_inverted_index":{"Abstract":[0],"Morgan":[1],"Ward":[2],"pursued":[3],"the":[4],"study":[5],"of":[6,30],"elliptic":[7,22],"divisibility":[8,23],"sequences,":[9],"originally":[10],"initiated":[11],"by":[12],"Lucas,":[13],"and":[14,16,43],"Chudnovsky":[15,17],"subsequently":[18],"suggested":[19],"looking":[20],"at":[21],"sequences":[24,35,59],"for":[25],"prime":[26,31],"appearance.":[27],"The":[28],"problem":[29],"appearance":[32],"in":[33],"these":[34,58],"is":[36],"examined":[37],"here,":[38],"from":[39],"both":[40],"a":[41,44,52],"theoretical":[42],"practical":[45],"viewpoint.":[46],"We":[47],"show":[48],"calculations,":[49],"together":[50],"with":[51],"heuristic":[53],"argument,":[54],"to":[55],"suggest":[56],"that":[57],"contain":[60],"only":[61],"finitely":[62],"many":[63],"primes.":[64]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}