{"id":"https://openalex.org/W2912995451","doi":"https://doi.org/10.1090/s0025-5718-00-01197-2","title":"Frobenius pseudoprimes","display_name":"Frobenius pseudoprimes","publication_year":2000,"publication_date":"2000-03-01","ids":{"openalex":"https://openalex.org/W2912995451","doi":"https://doi.org/10.1090/s0025-5718-00-01197-2","mag":"2912995451"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01197-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01197-2","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01197-2/S0025-5718-00-01197-2.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01197-2/S0025-5718-00-01197-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jon Grantham","orcid":null},"institutions":[{"id":"https://openalex.org/I3149230897","display_name":"Institute For Defense Analyses","ror":"https://ror.org/00rh8m666","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I3149230897"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jon Grantham","raw_affiliation_strings":["Institute for Defense Analyses, Center for Computing Sciences, 17100 Science Drive, Bowie, MD 20715"],"affiliations":[{"raw_affiliation_string":"Institute for Defense Analyses, Center for Computing Sciences, 17100 Science Drive, Bowie, MD 20715","institution_ids":["https://openalex.org/I3149230897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I3149230897"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.42092358,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"70","issue":"234","first_page":"873","last_page":"891"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.7925999760627747,"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":0.7925999760627747,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.13740000128746033,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.01269999984651804,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5983999967575073},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5393999814987183},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.43779999017715454},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3467000126838684},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.33160001039505005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9146999716758728},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5983999967575073},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38179999589920044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3467000126838684},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2768000066280365},{"id":"https://openalex.org/C154977054","wikidata":"https://www.wikidata.org/wiki/Q1759646","display_name":"Lucas sequence","level":5,"score":0.2451000064611435}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-00-01197-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01197-2","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01197-2/S0025-5718-00-01197-2.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:arXiv.org:1903.06820","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.06820","pdf_url":"https://arxiv.org/pdf/1903.06820","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01197-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01197-2","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01197-2/S0025-5718-00-01197-2.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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2912995451.pdf","grobid_xml":"https://content.openalex.org/works/W2912995451.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W180506625","https://openalex.org/W6601328927","https://openalex.org/W6601573739"],"related_works":[],"abstract_inverted_index":{"The":[0],"proliferation":[1],"of":[2,13,46,53,59,68,75,78,84,97,102,110,123],"probable":[3],"prime":[4],"tests":[5,42,80],"in":[6,19,94,117],"recent":[7],"years":[8],"has":[9],"produced":[10],"a":[11,44,51,60,73,85],"plethora":[12],"definitions":[14,54],"with":[15],"the":[16,66,95,103,108],"word":[17],"\u201cpseudoprime\u201d":[18],"them.":[20],"Examples":[21],"include":[22],"pseudoprimes,":[23,25,27,29,32],"Euler":[24],"strong":[26,30,34],"Lucas":[28,31,35],"extra":[33],"pseudoprimes":[36],"and":[37],"Perrin":[38],"pseudoprimes.":[39,124],"Though":[40],"these":[41,79],"represent":[43],"wealth":[45],"ideas,":[47],"they":[48],"exist":[49],"as":[50,57,81,88,90],"hodge-podge":[52],"rather":[55],"than":[56],"examples":[58],"more":[61],"general":[62,86],"theory.":[63],"It":[64],"is":[65,105,114],"goal":[67],"this":[69],"paper":[70],"to":[71,91,106,115],"present":[72],"way":[74],"viewing":[76],"many":[77],"special":[82],"cases":[83],"principle,":[87],"well":[89],"re-formulate":[92],"them":[93],"context":[96],"finite":[98],"fields.":[99],"One":[100],"aim":[101],"reformulation":[104],"enable":[107],"creation":[109],"stronger":[111],"tests;":[112],"another":[113],"aid":[116],"proving":[118],"results":[119],"about":[120],"large":[121],"classes":[122]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2019-02-21T00:00:00"}