乐胖代购免代理版

{"id":"https://openalex.org/W2884734563","doi":"https://doi.org/10.1090/mcom/3501","title":"Two algorithms to find primes in patterns","display_name":"Two algorithms to find primes in patterns","publication_year":2019,"publication_date":"2019-12-04","ids":{"openalex":"https://openalex.org/W2884734563","doi":"https://doi.org/10.1090/mcom/3501","mag":"2884734563"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3501","pdf_url":"https://www.ams.org/mcom/2020-89-324/S0025-5718-2020-03501-7/S0025-5718-2020-03501-7.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},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ams.org/mcom/2020-89-324/S0025-5718-2020-03501-7/S0025-5718-2020-03501-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025020420","display_name":"Jonathan Sorenson","orcid":"https://orcid.org/0000-0002-8887-5957"},"institutions":[{"id":"https://openalex.org/I110678235","display_name":"Butler University","ror":"https://ror.org/05gq3a412","country_code":"US","type":"education","lineage":["https://openalex.org/I110678235"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan P. Sorenson","raw_affiliation_strings":["Department of Computer Science and Software Engineering, Butler University, Indianapolis, Indiana 46208"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Software Engineering, Butler University, Indianapolis, Indiana 46208","institution_ids":["https://openalex.org/I110678235"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087016197","display_name":"Jonathan Webster","orcid":null},"institutions":[{"id":"https://openalex.org/I110678235","display_name":"Butler University","ror":"https://ror.org/05gq3a412","country_code":"US","type":"education","lineage":["https://openalex.org/I110678235"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Webster","raw_affiliation_strings":["Department of Mathematics, Statistics, and Actuarial Science, Butler University, Indianapolis, Indiana 46208"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Actuarial Science, Butler University, Indianapolis, Indiana 46208","institution_ids":["https://openalex.org/I110678235"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.342,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":4,"citation_normalized_percentile":{"value":0.567917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":77,"max":79},"biblio":{"volume":"89","issue":"324","first_page":"1953","last_page":"1968"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9999,"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":0.9999,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9978,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/constant","display_name":"Constant (computer programming)","score":0.43036383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8010251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.63827044},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.60127074},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.58691597},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.53511363},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5050362},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.46708107},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.45669135},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43036383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40867588},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40231875},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3220748},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07368919},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3501","pdf_url":"https://www.ams.org/mcom/2020-89-324/S0025-5718-2020-03501-7/S0025-5718-2020-03501-7.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},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1807.08777","pdf_url":"https://arxiv.org/pdf/1807.08777","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.1807.08777","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3501","pdf_url":"https://www.ams.org/mcom/2020-89-324/S0025-5718-2020-03501-7/S0025-5718-2020-03501-7.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},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":["https://openalex.org/W2884734563"],"referenced_works_count":42,"referenced_works":["https://openalex.org/W1479917419","https://openalex.org/W1480319329","https://openalex.org/W1551619147","https://openalex.org/W1555475515","https://openalex.org/W1582466057","https://openalex.org/W1812494664","https://openalex.org/W1894661220","https://openalex.org/W1980350947","https://openalex.org/W1986624837","https://openalex.org/W2005936791","https://openalex.org/W2011228818","https://openalex.org/W2012857639","https://openalex.org/W2015669348","https://openalex.org/W2017309658","https://openalex.org/W2033727285","https://openalex.org/W2037363226","https://openalex.org/W2041802178","https://openalex.org/W2071056578","https://openalex.org/W2071743058","https://openalex.org/W2076597612","https://openalex.org/W2090725688","https://openalex.org/W2150462872","https://openalex.org/W2153420132","https://openalex.org/W2159341052","https://openalex.org/W2166856074","https://openalex.org/W2170413523","https://openalex.org/W2316210826","https://openalex.org/W2566275643","https://openalex.org/W2908533878","https://openalex.org/W2962847573","https://openalex.org/W3101706508","https://openalex.org/W3175367423","https://openalex.org/W4230211117","https://openalex.org/W4231463924","https://openalex.org/W4241030354","https://openalex.org/W4245074849","https://openalex.org/W4253677563","https://openalex.org/W4254378619","https://openalex.org/W4296300736","https://openalex.org/W4302383489","https://openalex.org/W4388288416","https://openalex.org/W820979427"],"related_works":["https://openalex.org/W4387070058","https://openalex.org/W4315481288","https://openalex.org/W4281800544","https://openalex.org/W4232276891","https://openalex.org/W3112335383","https://openalex.org/W3101321773","https://openalex.org/W306052976","https://openalex.org/W2047954281","https://openalex.org/W2046177514","https://openalex.org/W2003101256"],"abstract_inverted_index":{"Let":[0],"$k\\ge":[1],"1$":[2],"be":[3,13],"an":[4],"integer,":[5],"and":[6,40,141],"let":[7],"$P=":[8],"(f_1(x),":[9],"\\ldots,":[10],"f_k(x)":[11],")$":[12],"$k$":[14],"admissible":[15],"linear":[16],"polynomials":[17],"over":[18],"the":[19,42,85,107],"integers,":[20],"or":[21],"\\textit{the":[22],"pattern}.":[23],"We":[24,80,95,113],"present":[25],"two":[26,90],"algorithms":[27],"that":[28],"find":[29],"all":[30,41,144],"integers":[31],"$x$":[32],"where":[33],"$\\max{":[34],"\\{f_i(x)":[35],"\\}":[36],"}":[37],"\\le":[38],"n$":[39],"$f_i(x)$":[43],"are":[44,96],"prime.":[45],"Our":[46,59],"first":[47],"algorithm":[48,61,122],"takes":[49,62],"at":[50],"most":[51],"$O_P(n/(\\log\\log":[52],"n)^k)$":[53],"arithmetic":[54,69],"operations":[55],"using":[56],"$O(k\\sqrt{n})$":[57],"space.":[58],"second":[60,121],"slightly":[63],"more":[64],"time,":[65],"$O_P(n/(\\log":[66],"\\log":[67],"n)^{k-1})$":[68],"operations,":[70],"but":[71,84,92],"uses":[72],"only":[73],"$n^{1/c}$":[74],"space":[75],"for":[76,103],"a":[77,110],"constant":[78],"$c>2$.":[79],"prove":[81],"correctness":[82],"unconditionally,":[83],"running":[86],"time":[87],"relies":[88],"on":[89],"unproven":[91],"reasonable":[93],"conjectures.":[94],"unaware":[97],"of":[98,109,119,138],"any":[99],"previous":[100],"complexity":[101],"results":[102],"this":[104],"problem":[105],"beyond":[106],"use":[108],"prime":[111],"sieve.":[112],"also":[114],"implemented":[115],"several":[116],"parallel":[117],"versions":[118],"our":[120],"to":[123,148],"show":[124],"it":[125],"is":[126],"viable":[127],"in":[128],"practice.":[129],"In":[130],"particular,":[131],"we":[132,142],"found":[133,143],"some":[134],"new":[135],"Cunningham":[136],"chains":[137],"length":[139],"15,":[140],"quadruplet":[145],"primes":[146],"up":[147],"$10^{17}$.":[149]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2884734563","counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2025-01-02T15:50:05.771984","created_date":"2018-08-03"}