{"id":"https://openalex.org/W2009029861","doi":"https://doi.org/10.1090/s0025-5718-96-00692-8","title":"A new algorithm for constructing large Carmichael numbers","display_name":"A new algorithm for constructing large Carmichael numbers","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2009029861","doi":"https://doi.org/10.1090/s0025-5718-96-00692-8","mag":"2009029861"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-96-00692-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00692-8","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00692-8/S0025-5718-96-00692-8.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/1996-65-214/S0025-5718-96-00692-8/S0025-5718-96-00692-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053260903","display_name":"G\u00fcnter L\u00f6h","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"G\u00fcnter L\u00f6h","raw_affiliation_strings":["Regionales Rechenzentrum der Universit\u00e4t Hamburg, Schl\u00fcterstra\u00dfe 70, 20146 Hamburg, Germany"],"affiliations":[{"raw_affiliation_string":"Regionales Rechenzentrum der Universit\u00e4t Hamburg, Schl\u00fcterstra\u00dfe 70, 20146 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065444791","display_name":"Wolfgang Niebuhr","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wolfgang Niebuhr","raw_affiliation_strings":["Lisztstra\u00c3\u009fe 6b, 22763 Hamburg, Germany","Regionales Rechenzentrum der Universit\u00c3\u00a4t Hamburg, Schl\u00c3\u00bcterstra\u00c3\u009fe 70, 20146 Hamburg, Germany"],"affiliations":[{"raw_affiliation_string":"Lisztstra\u00c3\u009fe 6b, 22763 Hamburg, Germany","institution_ids":[]},{"raw_affiliation_string":"Regionales Rechenzentrum der Universit\u00c3\u00a4t Hamburg, Schl\u00c3\u00bcterstra\u00c3\u009fe 70, 20146 Hamburg, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053260903"],"corresponding_institution_ids":["https://openalex.org/I159176309"],"apc_list":null,"apc_paid":null,"fwci":0.7669,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.6468254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"65","issue":"214","first_page":"823","last_page":"836"},"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/T11428","display_name":"Advanced Mathematical Identities","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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9977999925613403,"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/algorithm","display_name":"Algorithm","score":0.739439845085144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4330097734928131},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4310920238494873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32146209478378296}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.739439845085144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4330097734928131},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4310920238494873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32146209478378296}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-96-00692-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00692-8","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00692-8/S0025-5718-96-00692-8.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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00692-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00692-8","pdf_url":"https://www.ams.org/mcom/1996-65-214/S0025-5718-96-00692-8/S0025-5718-96-00692-8.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/W2009029861.pdf","grobid_xml":"https://content.openalex.org/works/W2009029861.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W45884410","https://openalex.org/W59107885","https://openalex.org/W66910720","https://openalex.org/W289732966","https://openalex.org/W1514415888","https://openalex.org/W1516779336","https://openalex.org/W1547493220","https://openalex.org/W1980350947","https://openalex.org/W2000422262","https://openalex.org/W2015669348","https://openalex.org/W2034667677","https://openalex.org/W2042826500","https://openalex.org/W2047316746","https://openalex.org/W2047359249","https://openalex.org/W2057182494","https://openalex.org/W2075488055","https://openalex.org/W2076597612","https://openalex.org/W2086752754","https://openalex.org/W2166856074","https://openalex.org/W2324192779","https://openalex.org/W2327071805","https://openalex.org/W2327162874","https://openalex.org/W2330778380","https://openalex.org/W2752853835","https://openalex.org/W3158027121","https://openalex.org/W3175367423","https://openalex.org/W4230643167","https://openalex.org/W4234026051","https://openalex.org/W4253237204","https://openalex.org/W4254378619","https://openalex.org/W6602699540","https://openalex.org/W6632818173"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"We":[0,223],"describe":[1],"an":[2],"algorithm":[3,85],"for":[4],"constructing":[5],"Carmichael":[6,194,225],"numbers":[7,226],"<inline-formula":[8,28,91,196,230],"content-type=\"math/mathml\">":[9,29,92,197,231],"<mml:math":[10,30,93,198,232],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,31,94,199,233],"alttext=\"upper":[12],"N\">":[13],"<mml:semantics>":[14,44,122,205,235],"<mml:mi>N</mml:mi>":[15,212],"<mml:annotation":[16,74,177,216,237],"encoding=\"application/x-tex\">N</mml:annotation>":[17],"</mml:semantics>":[18,80,185,219,239],"</mml:math>":[19,81,186,220,240],"</inline-formula>":[20,82,187,221,241],"with":[21,87,227],"a":[22,88],"large":[23],"number":[24,90],"of":[25,192],"prime":[26],"factors":[27],"alttext=\"p":[32],"1":[33,104,106,111,120],"comma":[34,37,39,107,112,114],"p":[35,40,103,108,115],"2":[36,109],"ellipsis":[38,113],"Subscript":[41,116],"k":[42,117],"Baseline\">":[43],"<mml:mrow>":[45,123,206],"<mml:msub>":[46,54,66,135,147,163],"<mml:mi>p</mml:mi>":[47,55,67,136,148,164],"<mml:mrow":[48,56,68,137,149,165],"class=\"MJX-TeXAtom-ORD\">":[49,57,69,138,150,166],"<mml:mn>1</mml:mn>":[50,139,145,157,173],"</mml:mrow>":[51,59,71,73,140,152,168,176,215],"</mml:msub>":[52,60,72,141,153,169],"<mml:mo>,</mml:mo>":[53,61,65,146,158,162],"<mml:mn>2</mml:mn>":[58,151],"<mml:mo>":[62,130,142,154,159,170],"\u2026":[63,160],"</mml:mo>":[64,132,144,156,161,172],"<mml:mi>k</mml:mi>":[70,167],"encoding=\"application/x-tex\">p_{1},":[75],"p_{2},":[76],"\\dots":[77,183],",":[78,188],"p_{k}</mml:annotation>":[79],".":[83,222],"This":[84],"starts":[86],"given":[89],"alttext=\"normal":[95],"upper":[96,202],"Lamda":[97],"equals":[98],"l":[99],"c":[100],"m":[101],"left-parenthesis":[102,201],"minus":[105,110,119],"Baseline":[118],"right-parenthesis\">":[121,204],"<mml:mi":[124],"mathvariant=\"normal\">":[125],"\u039b":[126],"</mml:mi>":[127,209],"<mml:mo>=</mml:mo>":[128],"<mml:mi>lcm</mml:mi>":[129],"\u2061":[131],"<mml:mo":[133,174,210,213],"stretchy=\"false\">(</mml:mo>":[134,211],"\u2212":[143,155,171],"stretchy=\"false\">)</mml:mo>":[175,214],"encoding=\"application/x-tex\">\\Lambda":[178],"=\\operatorname":[179],"{lcm}":[180],"(p_{1}-1,":[181],"p_{2}-1,":[182],",p_{k}-1)</mml:annotation>":[184],"representing":[189],"the":[190,193],"value":[191],"function":[195],"alttext=\"lamda":[200],"N":[203],"<mml:mi>":[207],"\u03bb":[208],"encoding=\"application/x-tex\">\\lambda":[217],"(N)</mml:annotation>":[218],"found":[224],"up":[228],"to":[229],"alttext=\"1101518\">":[234],"<mml:mn>1101518</mml:mn>":[236],"encoding=\"application/x-tex\">1101518</mml:annotation>":[238],"factors.":[242]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
