{"id":"https://openalex.org/W7220413541","doi":"https://doi.org/10.48550/arxiv.2610.02550","title":"The Prime Wavelet Tree: Compressing the Carmichael Numbers","display_name":"The Prime Wavelet Tree: Compressing the Carmichael Numbers","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220413541","doi":"https://doi.org/10.48550/arxiv.2610.02550"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02550","pdf_url":"https://arxiv.org/pdf/2610.02550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02550","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070843690","display_name":"Ankur Gupta","orcid":"https://orcid.org/0000-0002-4651-5830","observed_orcids":["https://orcid.org/0000-0002-4651-5830"]},"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":"Gupta, Ankur","raw_affiliation_strings":["Dept. of Mathematical Sciences Software Engineering Butler University Butler University Indianapolis , IN , USA Indianapolis , IN , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematical Sciences Software Engineering Butler University Butler University Indianapolis , IN , USA Indianapolis , IN , USA","institution_ids":["https://openalex.org/I110678235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087016197","display_name":"Jonathan Webster","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Webster, Jonathan","raw_affiliation_strings":["Dept. of Computer Science and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science and","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012144778","display_name":"Sylvia Webster","orcid":null,"observed_orcids":[]},"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":"Webster, Sylvia","raw_affiliation_strings":["Dept. of Mathematical Sciences Software Engineering Butler University Butler University Indianapolis , IN , USA Indianapolis , IN , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematical Sciences Software Engineering Butler University Butler University Indianapolis , IN , USA Indianapolis , IN , USA","institution_ids":["https://openalex.org/I110678235"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9907000064849854,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9907000064849854,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.0024999999441206455,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0024999999441206455,"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/carmichael-numbers","display_name":"Carmichael numbers","score":0.9470000267028809},{"id":"https://openalex.org/keywords/pseudoprimes","display_name":"pseudoprimes","score":0.7860000133514404},{"id":"https://openalex.org/keywords/data-compression","display_name":"data compression","score":0.42899999022483826}],"concepts":[{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.640999972820282},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.6101999878883362},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5958999991416931},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.572700023651123},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5184000134468079},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4936000108718872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41510000824928284},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.40709999203681946},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4043000042438507},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32199999690055847},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.3012999892234802},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.30090001225471497},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2816999852657318},{"id":"https://openalex.org/C136968285","wikidata":"https://www.wikidata.org/wiki/Q3246374","display_name":"Set partitioning in hierarchical trees","level":5,"score":0.26350000500679016},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02550","pdf_url":"https://arxiv.org/pdf/2610.02550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.02550","doi":"https://doi.org/10.48550/arxiv.2610.02550","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02550","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02550","pdf_url":"https://arxiv.org/pdf/2610.02550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220413541.pdf","grobid_xml":"https://content.openalex.org/works/W7220413541.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1568325880","https://openalex.org/W2008969497","https://openalex.org/W2011228818","https://openalex.org/W4417308887","https://openalex.org/W7131643421"],"related_works":["https://openalex.org/W3166208120","https://openalex.org/W2324674507","https://openalex.org/W1614273003","https://openalex.org/W2096575760","https://openalex.org/W2210420966","https://openalex.org/W7030493174","https://openalex.org/W2994768150","https://openalex.org/W1554262189","https://openalex.org/W7071822639","https://openalex.org/W7119509980"],"abstract_inverted_index":{"We":[0,50],"present":[1],"two":[2],"number-theoretic":[3],"compression":[4,53,78],"techniques.":[5],"The":[6,14,99],"first":[7],"is":[8,16,31,89],"\\textit{local},":[9],"and":[10,18,80],"compresses":[11,19],"individual":[12],"numbers.":[13],"second":[15],"\\textit{global},":[17],"the":[20,56,86,96],"entire":[21],"set":[22,43],"of":[23,35,44,60,84],"numbers":[24,45,64,102],"using":[25,55],"a":[26,32,47,81],"\\textit{prime":[27],"wavelet":[28],"tree},":[29],"which":[30],"data":[33],"structure":[34],"independent":[36],"interest.":[37],"Our":[38],"techniques":[39,54,79],"apply":[40],"to":[41],"any":[42],"satisfying":[46],"Korselt-like":[48],"criterion.":[49],"demonstrate":[51],"our":[52],"recently":[57],"completed":[58],"tabulation":[59],"all":[61],"$308{,}279{,}939$":[62],"Carmichael":[63],"less":[65],"than":[66,95],"$10^{24}$":[67],"that":[68],"occupies":[69],"$18.4$":[70],"gigabytes":[71],"as":[72],"text.":[73],"When":[74],"combined":[75],"with":[76],"standard":[77],"heuristic":[82],"choice":[83],"divisors,":[85],"resulting":[87],"file":[88],"$588.7$":[90],"megabytes":[91],"($31.2$":[92],"times":[93],"smaller":[94],"text":[97],"file).":[98],"initial":[100],"$80$-bit":[101],"now":[103],"use":[104],"about":[105],"$15.3$":[106],"bits.":[107]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}