{"id":"https://openalex.org/W197511432","doi":null,"title":"Prime Numbers are Infinitely Many: Four Proofs from History to Mathematics Education","display_name":"Prime Numbers are Infinitely Many: Four Proofs from History to Mathematics Education","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W197511432","mag":"197511432"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.564.6028","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.564.6028","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.syllogismos.it/history/Icme10-TSG17.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5036697320","display_name":"Giorgio Tomaso Bagni","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giorgio T. Bagni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5036697320"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/euclid-s-proof","display_name":"Euclid's proof","score":0.8140000104904175},{"id":"https://openalex.org/keywords/history-of-mathematics","display_name":"history of mathematics","score":0.8040000200271606},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"mathematics education","score":0.7850000262260437},{"id":"https://openalex.org/keywords/epistemology-of-mathematics","display_name":"epistemology of mathematics","score":0.7440000176429749},{"id":"https://openalex.org/keywords/historical-analysis","display_name":"historical analysis","score":0.4970000088214874},{"id":"https://openalex.org/keywords/proof-techniques","display_name":"proof techniques","score":0.7009999752044678},{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":0.43799999356269836}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.786941647529602},{"id":"https://openalex.org/C72074766","wikidata":"https://www.wikidata.org/wiki/Q185264","display_name":"History of mathematics","level":2,"score":0.6012236475944519},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5472643971443176},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.5316738486289978},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4358103275299072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4190177321434021},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.33624380826950073},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3242151439189911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3221445679664612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08746352791786194},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07409641146659851},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.564.6028","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.564.6028","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.syllogismos.it/history/Icme10-TSG17.pdf","raw_type":"text"},{"id":"mag:197511432","doi":null,"is_oa":false,"landing_page_url":"http://www.syllogismos.it/history/Icme10-TSG17.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6164000034332275,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W98408535","https://openalex.org/W432875554","https://openalex.org/W1519565561","https://openalex.org/W1536022883","https://openalex.org/W1562180703","https://openalex.org/W1575818250","https://openalex.org/W1852876996","https://openalex.org/W1952841069","https://openalex.org/W2042137662","https://openalex.org/W2068028167","https://openalex.org/W2072267223","https://openalex.org/W2090353397","https://openalex.org/W2111158824","https://openalex.org/W2169575103","https://openalex.org/W2314559381","https://openalex.org/W2328612796","https://openalex.org/W2985025624","https://openalex.org/W3152784682","https://openalex.org/W3175502364"],"related_works":["https://openalex.org/W2038975271","https://openalex.org/W2920844026","https://openalex.org/W3026195294","https://openalex.org/W3129039499","https://openalex.org/W2632158468","https://openalex.org/W2953085731","https://openalex.org/W2611738389","https://openalex.org/W7099889762","https://openalex.org/W1444556082","https://openalex.org/W2794837540"],"abstract_inverted_index":{"Summary.":[0],"The":[1],"use":[2,39],"of":[3,27,40,58,70],"History":[4],"into":[5,43],"Mathematics":[6,44],"Education":[7],"links":[8],"teaching-learning":[9],"processes":[10],"with":[11,23,87],"historical":[12,25,41,79],"elements.":[13],"In":[14,46],"this":[15],"paper":[16],"we":[17,48,66],"discuss":[18],"some":[19,50,71],"epistemological":[20],"issues":[21],"related":[22],"the":[24,55,59,68],"analysis":[26],"a":[28,85],"mathematical":[29],"topic,":[30],"in":[31,77,81],"order":[32,82],"to":[33,83,89],"achieve":[34],"an":[35],"effective":[36],"and":[37,53,62],"correct":[38,60],"data":[42],"Education.":[45],"particular":[47],"present":[49],"theoretical":[51,91],"frameworks":[52],"underline":[54],"primary":[56],"importance":[57],"social":[61],"cultural":[63],"contextualisation.":[64],"Finally,":[65],"propose":[67],"comparison":[69],"different":[72,78],"strategies":[73],"used":[74],"by":[75],"mathematicians":[76],"periods":[80],"prove":[84],"theorem,":[86],"reference":[88],"presented":[90],"frameworks.":[92]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}