{"id":"https://openalex.org/W2056180212","doi":"https://doi.org/10.1090/s0025-5718-08-02170-4","title":"Ten new primitive binary trinomials","display_name":"Ten new primitive binary trinomials","publication_year":2008,"publication_date":"2008-08-01","ids":{"openalex":"https://openalex.org/W2056180212","doi":"https://doi.org/10.1090/s0025-5718-08-02170-4","mag":"2056180212"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02170-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02170-4","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02170-4/S0025-5718-08-02170-4.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/2009-78-266/S0025-5718-08-02170-4/S0025-5718-08-02170-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078366249","display_name":"Richard P. Brent","orcid":"https://orcid.org/0000-0002-8495-7437"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Richard Brent","raw_affiliation_strings":["Australian National University, Canberra, Australia","Australian Nat. University, Canberra, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Australian National University, Canberra, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"Australian Nat. University, Canberra, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057843487","display_name":"Paul Zimmermann","orcid":"https://orcid.org/0000-0003-0718-4458"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paul Zimmermann","raw_affiliation_strings":["INRIA Nancy, Grand Est, Villers-l\u00c3\u00a8s-Nancy, France","Inria Nancy\u2010Grand Est Villers\u2010l\u00e8s\u2010Nancy France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Nancy, Grand Est, Villers-l\u00c3\u00a8s-Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Inria Nancy\u2010Grand Est Villers\u2010l\u00e8s\u2010Nancy France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078366249"],"corresponding_institution_ids":["https://openalex.org/I118347636"],"apc_list":null,"apc_paid":null,"fwci":4.7003,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94494124,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"78","issue":"266","first_page":"1197","last_page":"1199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.996999979019165,"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/trinomial","display_name":"Trinomial","score":0.9760279655456543},{"id":"https://openalex.org/keywords/mersenne-prime","display_name":"Mersenne prime","score":0.9086921215057373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8400267362594604},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6264111995697021},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5494845509529114},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3728994131088257},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3331427574157715}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.9760279655456543},{"id":"https://openalex.org/C29641680","wikidata":"https://www.wikidata.org/wiki/Q186875","display_name":"Mersenne prime","level":2,"score":0.9086921215057373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8400267362594604},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6264111995697021},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5494845509529114},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3728994131088257},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3331427574157715}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-08-02170-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02170-4","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02170-4/S0025-5718-08-02170-4.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:HAL:inria-00337525v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00337525","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02170-4/home.html","raw_type":"Journal articles"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/100237","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/100237","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02170-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02170-4","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02170-4/S0025-5718-08-02170-4.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":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2056180212.pdf","grobid_xml":"https://content.openalex.org/works/W2056180212.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2006157923","https://openalex.org/W2017058910","https://openalex.org/W2018043194","https://openalex.org/W2038582458","https://openalex.org/W2079168443","https://openalex.org/W2094836964","https://openalex.org/W2116078937","https://openalex.org/W2133165761","https://openalex.org/W2403172928","https://openalex.org/W2907132709","https://openalex.org/W4232983163"],"related_works":["https://openalex.org/W2051693161","https://openalex.org/W2402258364","https://openalex.org/W2105612371","https://openalex.org/W4297813257","https://openalex.org/W2048580218","https://openalex.org/W2017058910","https://openalex.org/W2056180212","https://openalex.org/W1630688314","https://openalex.org/W2079168443","https://openalex.org/W2156800894"],"abstract_inverted_index":{"We":[0],"exhibit":[1],"ten":[2],"new":[3],"primitive":[4],"trinomials":[5],"over":[6],"GF(2)":[7],"of":[8],"record":[9],"degrees":[10],"<inline-formula":[11,34,57,81],"content-type=\"math/mathml\">":[12,35,58,82],"<mml:math":[13,36,59,83],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,37,60,84],"alttext=\"24":[15],"036":[16],"583\">":[17],"<mml:semantics>":[18,41,64,88],"<mml:mrow>":[19,42,65,89],"<mml:mn>24</mml:mn>":[20],"<mml:mspace":[21,24,44,47,67,70,91,94],"width=\"thinmathspace\"/>":[22,25,45,48,68,71,92,95],"<mml:mn>036</mml:mn>":[23],"<mml:mn>583</mml:mn>":[26],"</mml:mrow>":[27,50,73,97],"<mml:annotation":[28,51,74,98],"encoding=\"application/x-tex\">24\\,036\\,583</mml:annotation>":[29],"</mml:semantics>":[30,53,76,100],"</mml:math>":[31,54,77,101],"</inline-formula>":[32,55,78,102],",":[33,56,79],"alttext=\"25":[38],"964":[39],"951\">":[40],"<mml:mn>25</mml:mn>":[43],"<mml:mn>964</mml:mn>":[46],"<mml:mn>951</mml:mn>":[49],"encoding=\"application/x-tex\">25\\,964\\,951</mml:annotation>":[52],"alttext=\"30":[61],"402":[62],"457\">":[63],"<mml:mn>30</mml:mn>":[66],"<mml:mn>402</mml:mn>":[69],"<mml:mn>457</mml:mn>":[72],"encoding=\"application/x-tex\">30\\,402\\,457</mml:annotation>":[75],"and":[80],"alttext=\"32":[85],"582":[86],"657\">":[87],"<mml:mn>32</mml:mn>":[90],"<mml:mn>582</mml:mn>":[93],"<mml:mn>657</mml:mn>":[96],"encoding=\"application/x-tex\">32\\,582\\,657</mml:annotation>":[99],".":[103],"This":[104],"completes":[105],"the":[106,109],"search":[107],"for":[108],"currently":[110],"known":[111],"Mersenne":[112],"prime":[113],"exponents.":[114]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}