{"id":"https://openalex.org/W561113958","doi":"https://doi.org/10.1007/s10623-015-0088-0","title":"Some primality tests that eluded Lucas","display_name":"Some primality tests that eluded Lucas","publication_year":2015,"publication_date":"2015-05-09","ids":{"openalex":"https://openalex.org/W561113958","doi":"https://doi.org/10.1007/s10623-015-0088-0","mag":"561113958"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-015-0088-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-015-0088-0","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016453919","display_name":"Eric L. F. Roettger","orcid":null},"institutions":[{"id":"https://openalex.org/I870124129","display_name":"Mount Royal University","ror":"https://ror.org/04evsam41","country_code":"CA","type":"education","lineage":["https://openalex.org/I870124129"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"E. L. Roettger","raw_affiliation_strings":["Department of General Education, Mount Royal University, Calgary, Canada"],"affiliations":[{"raw_affiliation_string":"Department of General Education, Mount Royal University, Calgary, Canada","institution_ids":["https://openalex.org/I870124129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020273160","display_name":"Hywel C Williams","orcid":"https://orcid.org/0000-0002-5646-3093"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"H. C. Williams","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Calgary, Calgary, Canada","Department of Mathematics and Statistics University of Calgary Calgary, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Calgary, Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Mathematics and Statistics University of Calgary Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109058495","display_name":"R. Kent Guy","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R. K. Guy","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Calgary, Calgary, Canada","Department of Mathematics and Statistics University of Calgary Calgary, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Calgary, Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Mathematics and Statistics University of Calgary Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016453919"],"corresponding_institution_ids":["https://openalex.org/I870124129"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.2403,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.53999071,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"77","issue":"2-3","first_page":"515","last_page":"539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994000196456909,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/primality-test","display_name":"Primality test","score":0.9582216739654541},{"id":"https://openalex.org/keywords/lucas-sequence","display_name":"Lucas sequence","score":0.6596107482910156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5728616118431091},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.515998363494873},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4975261986255646},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.44014471769332886},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41928568482398987},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.380839467048645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2986243963241577},{"id":"https://openalex.org/keywords/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.09942010045051575}],"concepts":[{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.9582216739654541},{"id":"https://openalex.org/C154977054","wikidata":"https://www.wikidata.org/wiki/Q1759646","display_name":"Lucas sequence","level":5,"score":0.6596107482910156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5728616118431091},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.515998363494873},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4975261986255646},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.44014471769332886},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41928568482398987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.380839467048645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2986243963241577},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.09942010045051575},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-015-0088-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-015-0088-0","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/5","score":0.5199999809265137,"display_name":"Gender equality"}],"awards":[{"id":"https://openalex.org/G5740495887","display_name":null,"funder_award_id":"6548","funder_id":"https://openalex.org/F4320321487","funder_display_name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320321487","display_name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W168432157","https://openalex.org/W230161078","https://openalex.org/W1565091248","https://openalex.org/W1989775869","https://openalex.org/W2021446977","https://openalex.org/W2036859942","https://openalex.org/W2048643528","https://openalex.org/W2058550050","https://openalex.org/W2064133253","https://openalex.org/W2094819751","https://openalex.org/W2314596157","https://openalex.org/W2328598177","https://openalex.org/W2328970987","https://openalex.org/W4238105952","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4243082029","https://openalex.org/W2091700477","https://openalex.org/W4388000982","https://openalex.org/W4382173243","https://openalex.org/W2702714904","https://openalex.org/W4254079709","https://openalex.org/W3095189540","https://openalex.org/W561113958","https://openalex.org/W4387772454","https://openalex.org/W2579704199"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}