{"id":"https://openalex.org/W2015779408","doi":"https://doi.org/10.1090/s0025-5718-01-01350-3","title":"Distribution of generalized Fermat prime numbers","display_name":"Distribution of generalized Fermat prime numbers","publication_year":2001,"publication_date":"2001-05-17","ids":{"openalex":"https://openalex.org/W2015779408","doi":"https://doi.org/10.1090/s0025-5718-01-01350-3","mag":"2015779408"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01350-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01350-3","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.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/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032979251","display_name":"Harvey Dubner","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Harvey Dubner","raw_affiliation_strings":["449 Beverly Road, Ridgewood, New Jersey 07450"],"affiliations":[{"raw_affiliation_string":"449 Beverly Road, Ridgewood, New Jersey 07450","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068827505","display_name":"Yves Gallot","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yves Gallot","raw_affiliation_strings":["12 bis rue Perrey, 31400 Toulouse, France"],"affiliations":[{"raw_affiliation_string":"12 bis rue Perrey, 31400 Toulouse, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032979251"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8582,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82465008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"71","issue":"238","first_page":"825","last_page":"832"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T12170","display_name":"History and Theory of Mathematics","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T13307","display_name":"Diverse Scientific and Engineering Research","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8606988191604614},{"id":"https://openalex.org/keywords/primality-test","display_name":"Primality test","score":0.8151288032531738},{"id":"https://openalex.org/keywords/fermats-last-theorem","display_name":"Fermat's Last Theorem","score":0.7150492668151855},{"id":"https://openalex.org/keywords/fermat-number","display_name":"Fermat number","score":0.5408338904380798},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.46167609095573425},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.41269171237945557},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3512347936630249}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8606988191604614},{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.8151288032531738},{"id":"https://openalex.org/C87670640","wikidata":"https://www.wikidata.org/wiki/Q132469","display_name":"Fermat's Last Theorem","level":2,"score":0.7150492668151855},{"id":"https://openalex.org/C171223647","wikidata":"https://www.wikidata.org/wiki/Q207264","display_name":"Fermat number","level":3,"score":0.5408338904380798},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.46167609095573425},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.41269171237945557},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3512347936630249}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-01-01350-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01350-3","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.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:CiteSeerX.psu:10.1.1.101.1387","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.101.1387","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.3861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01350-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01350-3","pdf_url":"https://www.ams.org/mcom/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2015779408.pdf","grobid_xml":"https://content.openalex.org/works/W2015779408.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W820979427","https://openalex.org/W1531131534","https://openalex.org/W1563654733","https://openalex.org/W1995945562","https://openalex.org/W2001339807","https://openalex.org/W2033727285","https://openalex.org/W2045826589","https://openalex.org/W2050602318","https://openalex.org/W2080984796","https://openalex.org/W2138180048","https://openalex.org/W2614431264","https://openalex.org/W2982077032","https://openalex.org/W3175367423","https://openalex.org/W4210917281","https://openalex.org/W4230211117","https://openalex.org/W4241295125","https://openalex.org/W4251092792","https://openalex.org/W4300914388","https://openalex.org/W4301795284","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W4214478600","https://openalex.org/W4250269883","https://openalex.org/W350270629","https://openalex.org/W4247762646","https://openalex.org/W2065958588","https://openalex.org/W132175232","https://openalex.org/W1790546275","https://openalex.org/W4286910198","https://openalex.org/W1931792851","https://openalex.org/W3012449447"],"abstract_inverted_index":{"Numbers":[0,59],"of":[1,69,82,115,157,160,166],"the":[2,66,83,138,167],"form":[3,84,156],"<inline-formula":[4,85,120],"content-type=\"math/mathml\">":[5,86,121],"<mml:math":[6,87,122],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,88,123],"alttext=\"upper":[8],"F":[9],"Subscript":[10],"b":[11,16],"comma":[12],"n":[13,21],"Baseline":[14,22,92],"equals":[15],"Superscript":[17,20,90],"2":[18],"Super":[19],"plus":[23],"1\">":[24,94],"<mml:semantics>":[25,95,125],"<mml:mrow>":[26,96],"<mml:msub>":[27],"<mml:mi>F</mml:mi>":[28],"<mml:mrow":[29,39],"class=\"MJX-TeXAtom-ORD\">":[30,40],"<mml:mi>b</mml:mi>":[31,38],"<mml:mo>,</mml:mo>":[32],"<mml:mi>n</mml:mi>":[33,43,126],"</mml:mrow>":[34,45,49,105],"</mml:msub>":[35],"<mml:mo>=</mml:mo>":[36],"<mml:msup>":[37,41,97],"<mml:mn>2</mml:mn>":[42,98],"</mml:msup>":[44,46,100],"<mml:mo>+</mml:mo>":[47],"<mml:mn>1</mml:mn>":[48,104],"<mml:annotation":[50,106,127],"encoding=\"application/x-tex\">F_{b,n}=b^{2^n}+1</mml:annotation>":[51],"</mml:semantics>":[52,108,129],"</mml:math>":[53,109,130],"</inline-formula>":[54,110,131],"are":[55,133,143],"called":[56],"Generalized":[57],"Fermat":[58],"(GFN).":[60],"A":[61,164],"computational":[62],"method":[63],"for":[64,118],"testing":[65,79],"probable":[67],"primality":[68],"a":[70,80],"GFN":[71,116,171],"is":[72,75,173],"described":[73],"which":[74],"as":[76,78],"fast":[77],"number":[81],"alttext=\"2":[89],"m":[91],"minus":[93],"<mml:mi>m</mml:mi>":[99],"<mml:mo>":[101],"\u2212":[102],"</mml:mo>":[103],"encoding=\"application/x-tex\">2^m-1</mml:annotation>":[107],".":[111],"The":[112,141],"theoretical":[113],"distributions":[114],"primes,":[117],"fixed":[119],"alttext=\"n\">":[124],"encoding=\"application/x-tex\">n</mml:annotation>":[128],",":[132],"derived":[134],"and":[135,146,153,162],"compared":[136],"to":[137,150],"actual":[139],"distributions.":[140],"predictions":[142],"surprisingly":[144],"accurate":[145],"can":[147],"be":[148],"used":[149],"support":[151],"Bateman":[152],"Horn\u2019s":[154],"quantitative":[155],"\u201cHypothesis":[158],"H\"":[159],"Schinzel":[161],"Sierpi\u0144ski.":[163],"list":[165],"current":[168],"largest":[169],"known":[170],"primes":[172],"included.":[174]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}