{"id":"https://openalex.org/W2119737270","doi":"https://doi.org/10.1007/978-3-540-87531-4_15","title":"Proving Infinitude of Prime Numbers Using Binomial Coefficients","display_name":"Proving Infinitude of Prime Numbers Using Binomial Coefficients","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2119737270","doi":"https://doi.org/10.1007/978-3-540-87531-4_15","mag":"2119737270"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-87531-4_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-87531-4_15","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5101813009","display_name":"Phuong Nguyen","orcid":"https://orcid.org/0000-0002-3752-8699"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Phuong Nguyen","raw_affiliation_strings":["University of Toronto, \u00a0","University of Toronto"],"affiliations":[{"raw_affiliation_string":"University of Toronto, \u00a0","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101813009"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.1504,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77839453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"184","last_page":"198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9901999831199646,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.7235931754112244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6083452701568604},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6006516814231873},{"id":"https://openalex.org/keywords/prime-number-theorem","display_name":"Prime number theorem","score":0.5815667510032654},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.5725472569465637},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5641941428184509},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.554713785648346},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5359804034233093},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.5314401984214783},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5185775756835938},{"id":"https://openalex.org/keywords/analytic-number-theory","display_name":"Analytic number theory","score":0.5182142853736877},{"id":"https://openalex.org/keywords/multiplicative-number-theory","display_name":"Multiplicative number theory","score":0.5133020281791687},{"id":"https://openalex.org/keywords/binomial-theorem","display_name":"Binomial theorem","score":0.5069973468780518},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4292146563529968},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.348233163356781},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3177553117275238},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.061533600091934204}],"concepts":[{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.7235931754112244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6083452701568604},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6006516814231873},{"id":"https://openalex.org/C40758505","wikidata":"https://www.wikidata.org/wiki/Q386292","display_name":"Prime number theorem","level":3,"score":0.5815667510032654},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.5725472569465637},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5641941428184509},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.554713785648346},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5359804034233093},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.5314401984214783},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5185775756835938},{"id":"https://openalex.org/C149381693","wikidata":"https://www.wikidata.org/wiki/Q10843274","display_name":"Analytic number theory","level":2,"score":0.5182142853736877},{"id":"https://openalex.org/C190565394","wikidata":"https://www.wikidata.org/wiki/Q6935001","display_name":"Multiplicative number theory","level":4,"score":0.5133020281791687},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.5069973468780518},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4292146563529968},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.348233163356781},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3177553117275238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.061533600091934204},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-540-87531-4_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-87531-4_15","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.219.3296","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.3296","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~ntp/studies/prime.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W9698083","https://openalex.org/W1572451808","https://openalex.org/W1587799979","https://openalex.org/W1607926272","https://openalex.org/W2052680294","https://openalex.org/W2071047533","https://openalex.org/W2088885554","https://openalex.org/W2119737270","https://openalex.org/W2169150716","https://openalex.org/W2170605748","https://openalex.org/W2319049567","https://openalex.org/W2951424111","https://openalex.org/W3103321781","https://openalex.org/W3128307576","https://openalex.org/W4248733413"],"related_works":["https://openalex.org/W3107955476","https://openalex.org/W4298858188","https://openalex.org/W2527294524","https://openalex.org/W2964343315","https://openalex.org/W2739012278","https://openalex.org/W4205761008","https://openalex.org/W4234740577","https://openalex.org/W3143801195","https://openalex.org/W2247138283","https://openalex.org/W3212457662"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}