{"id":"https://openalex.org/W2907910466","doi":"https://doi.org/10.1090/s0025-5718-2011-02489-0","title":"An \ud835\udc42(log\u00b2(\ud835\udc41)) time primality test for generalized Cullen numbers","display_name":"An \ud835\udc42(log\u00b2(\ud835\udc41)) time primality test for generalized Cullen numbers","publication_year":2011,"publication_date":"2011-03-11","ids":{"openalex":"https://openalex.org/W2907910466","doi":"https://doi.org/10.1090/s0025-5718-2011-02489-0","mag":"2907910466"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02489-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02489-0","pdf_url":"https://www.ams.org/mcom/2011-80-276/S0025-5718-2011-02489-0/S0025-5718-2011-02489-0.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2011-80-276/S0025-5718-2011-02489-0/S0025-5718-2011-02489-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005658480","display_name":"J. M. Grau","orcid":"https://orcid.org/0000-0001-6652-0509"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Grau","raw_affiliation_strings":["Department of Mathematics, University of Oviedo, Avda. Calvo Sotelo s/n, 33007, Oviedo, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, Avda. Calvo Sotelo s/n, 33007, Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001130113","display_name":"Antonio M. Oller\u2010Marc\u00e9n","orcid":"https://orcid.org/0000-0002-8191-3199"},"institutions":[{"id":"https://openalex.org/I255234318","display_name":"Universidad de Zaragoza","ror":"https://ror.org/012a91z28","country_code":"ES","type":"education","lineage":["https://openalex.org/I255234318"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antonio Oller-Marc\u00e9n","raw_affiliation_strings":["University of Zaragoza, Department of Mathematics, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Zaragoza, Department of Mathematics, C/Pedro Cerbuna 12, 50009 Zaragoza, Spain","institution_ids":["https://openalex.org/I255234318"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9067,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77352679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"80","issue":"276","first_page":"2315","last_page":"2323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5585913062095642},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33563682436943054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2895645201206207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26339542865753174}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5585913062095642},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33563682436943054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2895645201206207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26339542865753174}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-2011-02489-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02489-0","pdf_url":"https://www.ams.org/mcom/2011-80-276/S0025-5718-2011-02489-0/S0025-5718-2011-02489-0.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:digibuo.uniovi.es:10651/10978","is_oa":true,"landing_page_url":"http://hdl.handle.net/10651/10978","pdf_url":null,"source":{"id":"https://openalex.org/S4306402334","display_name":"Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educaci\u00f3n, Cultura y Deporte)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801976130","host_organization_name":"Ministerio de Educaci\u00f3n Cultura y Deporte","host_organization_lineage":["https://openalex.org/I2801976130"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02489-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02489-0","pdf_url":"https://www.ams.org/mcom/2011-80-276/S0025-5718-2011-02489-0/S0025-5718-2011-02489-0.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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/W2907910466.pdf","grobid_xml":"https://content.openalex.org/works/W2907910466.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1549276185","https://openalex.org/W1555475515","https://openalex.org/W1565091248","https://openalex.org/W1975619520","https://openalex.org/W2030340884","https://openalex.org/W2037760388","https://openalex.org/W2038620522","https://openalex.org/W2041727161","https://openalex.org/W2043282135","https://openalex.org/W2056599716","https://openalex.org/W2083368929","https://openalex.org/W2105443299","https://openalex.org/W2159341052","https://openalex.org/W2329291360","https://openalex.org/W2485612788","https://openalex.org/W4206503652","https://openalex.org/W4214850390","https://openalex.org/W4238450524","https://openalex.org/W4254280462","https://openalex.org/W6600906731"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Generalized":[0,131,181],"Cullen":[1,32,132,182],"Numbers":[2,33,133],"are":[3],"positive":[4],"integers":[5],"of":[6,31,42,53,130,180],"the":[7,50,127,178],"form":[8],"C":[9],"b":[10,16,59,66,71,90,91,101,102],"(":[11,62,160,164],"n":[12,15,17,58,60,70,72,93,94,107,108],")":[13,65,95,166,167],":=":[14],"+":[18,73],"1":[19,64,74],"C_b(n):=nb^n+1":[20],".":[21],"In":[22],"this":[23,40,56,112],"work":[24],"we":[25],"generalize":[26],"some":[27],"known":[28],"divisibility":[29],"properties":[30],"and":[34,80,92,96],"present":[35,137],"two":[36],"primality":[37],"tests":[38,151],"for":[39,111,143],"family":[41],"integers.":[43],"The":[44],"first":[45],"test":[46,87,99,114,142],"is":[47,78,103],"based":[48],"in":[49,157,177],"following":[51],"property":[52],"primes":[54],"from":[55],"family:":[57],"\u2261":[61],"\u2212":[63],"n^{b^{n}}\\equiv":[67],"(-1)^{b}":[68],"(mod":[69],"nb^n+1":[75],").":[76,109],"It":[77],"stronger":[79],"has":[81],"less":[82],"computational":[83],"cost":[84],"than":[85,97],"Fermat\u2019s":[86],"(to":[88],"bases":[89],"Miller-Rabin\u2019s":[98],"(if":[100],"odd,":[104],"to":[105,116,153],"base":[106],"Pseudoprimes":[110],"new":[113],"seem":[115],"be":[117,174],"very":[118,175],"scarce,":[119],"only":[120],"4":[121],"pseudoprimes":[122,146],"have":[123,147],"been":[124,148],"found":[125],"among":[126],"many":[128],"millions":[129],"tested.":[134],"We":[135],"also":[136],"a":[138],"second,":[139],"more":[140],"demanding,":[141],"which":[144,172],"no":[145],"found.":[149],"These":[150],"lead":[152],"an":[154],"algorithm,":[155],"running":[156],"O":[158],"~":[159],"log":[161],"2":[162],"\u2061":[163],"N":[165],"\\tilde":[168],"{O}(\\log":[169],"^2(N))":[170],"time,":[171],"might":[173],"useful":[176],"search":[179],"Primes.":[183]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2019-01-11T00:00:00"}
