{"id":"https://openalex.org/W4415420743","doi":"https://doi.org/10.15439/2025f0998","title":"A statistical hypothesis test for primality based on random divisor sampling: Principles, properties, adaptive design, and algorithmic analysis","display_name":"A statistical hypothesis test for primality based on random divisor sampling: Principles, properties, adaptive design, and algorithmic analysis","publication_year":2025,"publication_date":"2025-10-15","ids":{"openalex":"https://openalex.org/W4415420743","doi":"https://doi.org/10.15439/2025f0998"},"language":"en","primary_location":{"id":"doi:10.15439/2025f0998","is_oa":true,"landing_page_url":"https://doi.org/10.15439/2025f0998","pdf_url":"https://annals-csis.org/Volume_43/drp/pdf/0998.pdf","source":{"id":"https://openalex.org/S4220651875","display_name":"Annals of Computer Science and Information Systems","issn_l":"2300-5963","issn":["2300-5963"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310317484","host_organization_name":"Polskie Towarzystwo Informatyczne","host_organization_lineage":["https://openalex.org/P4310317484"],"host_organization_lineage_names":["Polskie Towarzystwo Informatyczne"],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Computer Science and Information Systems","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://annals-csis.org/Volume_43/drp/pdf/0998.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081142964","display_name":"Lubom\u00edr \u0160t\u011bp\u00e1nek","orcid":"https://orcid.org/0000-0002-8308-4304"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I4210089928","display_name":"Czech Academy of Sciences, Institute of Biophysics","ror":"https://ror.org/00angvn73","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210089928"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Lubom\u00edr \u0160t\u011bp\u00e1nek","raw_affiliation_strings":["Institute of Biophysics and Informatics, First Faculty of Medicine, Charles University"],"raw_orcid":"https://orcid.org/0000-0002-8308-4304","affiliations":[{"raw_affiliation_string":"Institute of Biophysics and Informatics, First Faculty of Medicine, Charles University","institution_ids":["https://openalex.org/I21250087","https://openalex.org/I4210089928"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081142964"],"corresponding_institution_ids":["https://openalex.org/I21250087","https://openalex.org/I4210089928"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30245144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":null,"first_page":"795","last_page":"800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/primality-test","display_name":"Primality test","score":0.8090999722480774},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.3808000087738037},{"id":"https://openalex.org/keywords/test","display_name":"Test (biology)","score":0.37929999828338623},{"id":"https://openalex.org/keywords/statistical-analysis","display_name":"Statistical analysis","score":0.3504999876022339},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2824999988079071}],"concepts":[{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.8090999722480774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5522000193595886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4763000011444092},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41200000047683716},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C2986587452","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical analysis","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30079999566078186},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28790000081062317},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.26829999685287476},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26350000500679016},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.15439/2025f0998","is_oa":true,"landing_page_url":"https://doi.org/10.15439/2025f0998","pdf_url":"https://annals-csis.org/Volume_43/drp/pdf/0998.pdf","source":{"id":"https://openalex.org/S4220651875","display_name":"Annals of Computer Science and Information Systems","issn_l":"2300-5963","issn":["2300-5963"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310317484","host_organization_name":"Polskie Towarzystwo Informatyczne","host_organization_lineage":["https://openalex.org/P4310317484"],"host_organization_lineage_names":["Polskie Towarzystwo Informatyczne"],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Computer Science and Information Systems","raw_type":"proceedings-article"},{"id":"pmh:oai:doaj.org/article:e87b7e4b319248dbb0610c660a619aa8","is_oa":true,"landing_page_url":"https://doaj.org/article/e87b7e4b319248dbb0610c660a619aa8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Annals of computer science and information systems, Vol 43, Pp 795-800 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.15439/2025f0998","is_oa":true,"landing_page_url":"https://doi.org/10.15439/2025f0998","pdf_url":"https://annals-csis.org/Volume_43/drp/pdf/0998.pdf","source":{"id":"https://openalex.org/S4220651875","display_name":"Annals of Computer Science and Information Systems","issn_l":"2300-5963","issn":["2300-5963"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310317484","host_organization_name":"Polskie Towarzystwo Informatyczne","host_organization_lineage":["https://openalex.org/P4310317484"],"host_organization_lineage_names":["Polskie Towarzystwo Informatyczne"],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Computer Science and Information Systems","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415420743.pdf","grobid_xml":"https://content.openalex.org/works/W4415420743.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1998777945","https://openalex.org/W2012857639","https://openalex.org/W2159341052","https://openalex.org/W2587027481","https://openalex.org/W4232836212","https://openalex.org/W4395661183"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,9,27,60,91,111,121,137,195],"statistical":[3],"hypothesis":[4,19],"test":[5,31,181],"for":[6,125],"determining":[7],"whether":[8,54],"given":[10,138],"integer":[11],"n":[12,24,70,176],"\u2265":[13],"2":[14],"is":[15,25,63,66,71,76,93,107,172,182],"prime.Under":[16],"the":[17,38,97,126,143],"null":[18],"H0,":[20],"we":[21],"assume":[22],"that":[23,163],"not":[26,67],"prime":[28],"(i.e.,":[29],"composite).The":[30],"operates":[32],"by":[33],"randomly":[34],"sampling":[35],"integers":[36],"from":[37],"candidate":[39],"divisor":[40,62,75,150],"set":[41,81],"D":[42],"=":[43,152],"{2,":[44],"3,":[45],".":[46,47],".,":[48],"\u230a":[49],"\u221a":[50,160],"n\u230b}":[51],"and":[52,69,90,114,186,193],"checking":[53],"any":[55],"of":[56,82,99,129,146,164],"them":[57],"divide":[58],"n.If":[59],"proper":[61],"found,":[64],"H0":[65,135],"rejected":[68],"declared":[72],"composite.If":[73],"no":[74],"found":[77],"among":[78],"an":[79,117,190],"initial":[80],"k0":[83],"samples,":[84],"additional":[85],"k":[86,131],"samples":[87],"are":[88],"drawn,":[89],"p-value":[92],"computed":[94],"based":[95],"on":[96],"probability":[98,106],"missing":[100],"all":[101],"actual":[102],"divisors":[103],"under":[104,142],"H0.This":[105],"calculated":[108],"exactly":[109],"via":[110],"hypergeometric":[112],"distribution":[113],"approximated":[115],"using":[116],"exponential":[118],"bound.We":[119],"derive":[120],"closed-form":[122],"upper":[123],"bound":[124],"minimal":[127],"number":[128],"trials":[130],"required":[132],"to":[133],"reject":[134],"at":[136],"significance":[139],"level":[140],"\u03b1":[141],"conservative":[144],"assumption":[145],"only":[147],"one":[148],"true":[149],"(m":[151],"1).The":[153],"algorithm":[154],"has":[155,177],"worst-case":[156],"time":[157],"complexity":[158],"O(":[159],"n),":[161],"matching":[162],"classical":[165],"trial":[166],"division,":[167],"but":[168],"its":[169],"expected":[170],"runtime":[171],"substantially":[173],"lower":[174],"when":[175],"multiple":[178],"divisors.The":[179],"proposed":[180],"simple,":[183],"statistically":[184],"interpretable,":[185],"well-suited":[187],"both":[188],"as":[189,194],"educational":[191],"tool":[192],"lightweight":[196],"probabilistic":[197],"pre-check":[198],"in":[199],"layered":[200],"primality":[201],"testing":[202],"pipelines.":[203]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-24T00:00:00"}
