{"id":"https://openalex.org/W2950140543","doi":"https://doi.org/10.3390/sym11060775","title":"An Investigation on the Prime and Twin Prime Number Functions by Periodical Binary Sequences and Symmetrical Runs in a Modified Sieve Procedure","display_name":"An Investigation on the Prime and Twin Prime Number Functions by Periodical Binary Sequences and Symmetrical Runs in a Modified Sieve Procedure","publication_year":2019,"publication_date":"2019-06-10","ids":{"openalex":"https://openalex.org/W2950140543","doi":"https://doi.org/10.3390/sym11060775","mag":"2950140543"},"language":"en","primary_location":{"id":"doi:10.3390/sym11060775","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060775","pdf_url":"https://www.mdpi.com/2073-8994/11/6/775/pdf?version=1561439346","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/6/775/pdf?version=1561439346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035398406","display_name":"Bruno Aiazzi","orcid":"https://orcid.org/0000-0003-3933-2320"},"institutions":[{"id":"https://openalex.org/I4210092323","display_name":"Nello Carrara Institute of Applied Physics","ror":"https://ror.org/00dqega85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210092323","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Bruno Aiazzi","raw_affiliation_strings":["Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]},{"raw_affiliation_string":"Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061007254","display_name":"Stefano Baronti","orcid":"https://orcid.org/0000-0003-0492-0886"},"institutions":[{"id":"https://openalex.org/I4210092323","display_name":"Nello Carrara Institute of Applied Physics","ror":"https://ror.org/00dqega85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210092323","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Baronti","raw_affiliation_strings":["Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]},{"raw_affiliation_string":"Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036568903","display_name":"Leonardo Santurri","orcid":"https://orcid.org/0000-0001-7316-643X"},"institutions":[{"id":"https://openalex.org/I4210092323","display_name":"Nello Carrara Institute of Applied Physics","ror":"https://ror.org/00dqega85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210092323","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Leonardo Santurri","raw_affiliation_strings":["Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]},{"raw_affiliation_string":"Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064642130","display_name":"Massimo Selva","orcid":"https://orcid.org/0000-0003-3202-5029"},"institutions":[{"id":"https://openalex.org/I4210092323","display_name":"Nello Carrara Institute of Applied Physics","ror":"https://ror.org/00dqega85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210092323","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimo Selva","raw_affiliation_strings":["Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Physics \u201dNello Carrara\u201d, IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]},{"raw_affiliation_string":"Institute of Applied Physics \"Nello Carrara\", IFAC-CNR, Research Area of Florence, 50019 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210092323"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035398406"],"corresponding_institution_ids":["https://openalex.org/I4210092323"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4406,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79738562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"11","issue":"6","first_page":"775","last_page":"775"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9965000152587891,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/twin-prime","display_name":"Twin prime","score":0.8673597574234009},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8234392404556274},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.635226845741272},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6011731028556824},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.5758500695228577},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5527938604354858},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5527387261390686},{"id":"https://openalex.org/keywords/sieve","display_name":"Sieve (category theory)","score":0.5476429462432861},{"id":"https://openalex.org/keywords/prime-number-theorem","display_name":"Prime number theorem","score":0.5186775922775269},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.48450490832328796},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.46875476837158203},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44738179445266724},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4321862459182739},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.4152716398239136},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2495003044605255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11753007769584656}],"concepts":[{"id":"https://openalex.org/C143352335","wikidata":"https://www.wikidata.org/wiki/Q110863","display_name":"Twin prime","level":3,"score":0.8673597574234009},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8234392404556274},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.635226845741272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6011731028556824},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.5758500695228577},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5527938604354858},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5527387261390686},{"id":"https://openalex.org/C17732976","wikidata":"https://www.wikidata.org/wiki/Q7511782","display_name":"Sieve (category theory)","level":2,"score":0.5476429462432861},{"id":"https://openalex.org/C40758505","wikidata":"https://www.wikidata.org/wiki/Q386292","display_name":"Prime number theorem","level":3,"score":0.5186775922775269},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.48450490832328796},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.46875476837158203},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44738179445266724},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4321862459182739},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.4152716398239136},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2495003044605255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11753007769584656},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11060775","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060775","pdf_url":"https://www.mdpi.com/2073-8994/11/6/775/pdf?version=1561439346","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:decf081200ff4ca8a2f8818ae89ba35a","is_oa":true,"landing_page_url":"https://doaj.org/article/decf081200ff4ca8a2f8818ae89ba35a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 6, p 775 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11060775","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060775","pdf_url":"https://www.mdpi.com/2073-8994/11/6/775/pdf?version=1561439346","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2950140543.pdf","grobid_xml":"https://content.openalex.org/works/W2950140543.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W770967448","https://openalex.org/W1488906634","https://openalex.org/W1495550473","https://openalex.org/W1675900842","https://openalex.org/W1711167705","https://openalex.org/W1966056204","https://openalex.org/W2032744364","https://openalex.org/W2045274883","https://openalex.org/W2054625478","https://openalex.org/W2068251997","https://openalex.org/W2071743058","https://openalex.org/W2095527188","https://openalex.org/W2106210395","https://openalex.org/W2150462872","https://openalex.org/W2178934104","https://openalex.org/W2493635557","https://openalex.org/W2788908493","https://openalex.org/W2938257243","https://openalex.org/W2964347707","https://openalex.org/W3101528528","https://openalex.org/W3201315942","https://openalex.org/W4242706295","https://openalex.org/W4252543992","https://openalex.org/W4292806204","https://openalex.org/W6637565906","https://openalex.org/W6722916708","https://openalex.org/W6747522923"],"related_works":["https://openalex.org/W2799791224","https://openalex.org/W2218160750","https://openalex.org/W2950823891","https://openalex.org/W4388468342","https://openalex.org/W3216551397","https://openalex.org/W161157439","https://openalex.org/W43753235","https://openalex.org/W2021497215","https://openalex.org/W1977732666","https://openalex.org/W3038435067"],"abstract_inverted_index":{"In":[0,174],"this":[1,39,175],"work,":[2],"the":[3,9,30,42,76,86,104,123,126,139,148,160,168,177,184,192,195,216,220,225,229,248,259],"Sieve":[4,12,105],"of":[5,20,29,38,44,65,75,88,103,114,116,122,183,194,231,238,261],"Eratosthenes":[6],"procedure":[7,40,179],"(in":[8],"following":[10],"named":[11,54],"procedure)":[13],"is":[14,23,47,53,118,135,156,172,189,210],"approached":[15],"by":[16,84,163,236,257],"a":[17,27,63,100,109,111,133,206,208],"novel":[18],"point":[19],"view,":[21],"which":[22,52],"able":[24,136],"to":[25,41,137,147,159,191,214,255],"give":[26],"justification":[28],"Prime":[31],"Number":[32],"Theorem":[33],"(P.N.T.).":[34],"Moreover,":[35],"an":[36,144,181,242],"extension":[37],"case":[43],"twin":[45,161,185,217,249],"primes":[46,218,250],"formulated.":[48],"The":[49,153],"proposed":[50,178],"investigation,":[51],"Limited":[55],"INtervals":[56],"into":[57,165],"PEriodical":[58],"Sequences":[59],"(LINPES)":[60],"relies":[61],"on":[62],"set":[64],"binary":[66],"periodical":[67],"sequences":[68,81],"that":[69,188,228],"are":[70,82,234],"evaluated":[71],"in":[72,99,107,120,129,143,212,219],"limited":[73],"intervals":[74,222,233],"prime":[77,140,186],"characteristic":[78],"function.":[79],"These":[80],"built":[83],"considering":[85],"ensemble":[87],"deleted":[89],"(that":[90,95],"is,":[91,96],"0)":[92],"and":[93],"undeleted":[94,127],"1)":[97],"integers":[98,128],"modified":[101],"version":[102],"procedure,":[106],"such":[108,241],"way":[110,146],"symmetric":[112],"succession":[113],"runs":[115,169],"zeroes":[117],"found":[119,223],"correspondence":[121],"gaps":[124],"between":[125],"each":[130],"period.":[131],"Such":[132],"formulation":[134],"estimate":[138],"number":[141],"function":[142,151,187,198],"equivalent":[145,190],"logarithmic":[149,196],"integral":[150,197],"Li(x).":[152],"present":[154],"analysis":[155],"then":[157,247],"extended":[158],"primes,":[162,239],"taking":[164],"account":[166],"only":[167],"whose":[170],"size":[171],"two.":[173],"case,":[176],"gives":[180],"estimation":[182],"one":[193],"Li":[199],"2":[200],"(":[201],"x":[202],")":[203],".":[204],"As":[205],"consequence,":[207],"possibility":[209],"investigated":[211],"order":[213],"count":[215],"same":[221],"for":[224],"primes.":[226],"Being":[227],"bounds":[230],"these":[232],"given":[235],"squares":[237],"if":[240],"inference":[243],"were":[244],"actually":[245],"proved,":[246],"could":[251],"be":[252],"estimated":[253],"up":[254],"infinity,":[256],"strengthening":[258],"conjecture":[260],"their":[262],"never-ending.":[263]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
