{"id":"https://openalex.org/W7214933922","doi":"https://doi.org/10.5281/zenodo.23064141","title":"ON TWO QUESTIONS OF ORDOWSKI ABOUT THE LARGEST EXPONENT IN A PRIME FACTORIZATION","display_name":"ON TWO QUESTIONS OF ORDOWSKI ABOUT THE LARGEST EXPONENT IN A PRIME FACTORIZATION","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7214933922","doi":"https://doi.org/10.5281/zenodo.23064141"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23064141","doi":"https://doi.org/10.5281/zenodo.23064141","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23064141","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23064141","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153487421","display_name":"Ansh Mishra","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mishra, Ansh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153540109","display_name":"Aryan Senthilkumar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Senthilkumar, Aryan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9800000190734863,"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":0.9800000190734863,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.006599999964237213,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.003700000001117587,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/wieferich-primes","display_name":"Wieferich primes","score":0.9629999995231628},{"id":"https://openalex.org/keywords/modular-exponentiation","display_name":"modular exponentiation","score":0.6639999747276306},{"id":"https://openalex.org/keywords/formal-verification","display_name":"formal verification","score":0.35100001096725464},{"id":"https://openalex.org/keywords/lean-4","display_name":"Lean 4","score":0.9509999752044678},{"id":"https://openalex.org/keywords/mathlib","display_name":"Mathlib","score":0.7900000214576721},{"id":"https://openalex.org/keywords/number-theory-conjectures","display_name":"number theory conjectures","score":0.5559999942779541}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7559000253677368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7070000171661377},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6280999779701233},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5989000201225281},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49000000953674316},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4867999851703644},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.4025000035762787},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.33410000801086426},{"id":"https://openalex.org/C18505202","wikidata":"https://www.wikidata.org/wiki/Q2654418","display_name":"Unique prime","level":4,"score":0.328000009059906},{"id":"https://openalex.org/C163540240","wikidata":"https://www.wikidata.org/wiki/Q936614","display_name":"Almost prime","level":4,"score":0.3052999973297119},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C185592164","wikidata":"https://www.wikidata.org/wiki/Q1052579","display_name":"Unique factorization domain","level":3,"score":0.29670000076293945},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.2915000021457672}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23064141","doi":"https://doi.org/10.5281/zenodo.23064141","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23064141","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.23064142","doi":"https://doi.org/10.5281/zenodo.23064142","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23064142","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.23064141","doi":"https://doi.org/10.5281/zenodo.23064141","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23064141","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4226200317","https://openalex.org/W7214455334","https://openalex.org/W2924392960","https://openalex.org/W2721312206","https://openalex.org/W7100383477","https://openalex.org/W7204652840","https://openalex.org/W7220678773","https://openalex.org/W2073568805","https://openalex.org/W4241097607","https://openalex.org/W2078892075"],"abstract_inverted_index":{"Let":[0],"a(n)":[1,25,79,93],"be":[2,81],"the":[3,7,60,101,112,134,147,153,159],"largest":[4],"exponent":[5],"in":[6,57,128],"prime":[8,77],"factorization":[9],"of":[10,59,115,139],"n":[11,23,35,105],"(OEIS":[12],"A051903).":[13],"In":[14],"2019":[15],"T.":[16,55],"Ordowski":[17],"asked":[18],"whether":[19],"there":[20],"are":[21,126],"odd":[22],"with":[24,111,131],">":[26],"1":[27],"such":[28],"that":[29,72],"(II)":[30,46],"b^n":[31],"=":[32,42,94,106,108],"b^a(n)":[33],"mod":[34,44],"for":[36],"all":[37,86,170],"b,":[38],"or":[39],"(III)":[40,73],"2^n":[41],"2^a(n)":[43],"n.":[45],"has":[47,74],"no":[48],"solutions.":[49,75],"This":[50],"was":[51],"observed":[52],"earlier":[53],"by":[54],"Adamczewski":[56],"reviews":[58],"Formal":[61,142],"Conjectures":[62,143],"statements,":[63],"and":[64,96,100,117,119,137,157,169],"we":[65],"give":[66],"a":[67,82,162],"lifting-the-exponent":[68],"proof.":[69],"We":[70],"show":[71],"The":[76,150],"attaining":[78],"must":[80],"Wieferich":[83,87,113],"prime.":[84],"For":[85],"primes":[88],"below":[89],"6.7*10^15":[90],"this":[91],"forces":[92],"2":[95],"square":[97],"part":[98],"3511^2,":[99],"smallest":[102],"solution":[103],"is":[104],"7*631*881*3511^2*201961":[107],"9687963167864344937,":[109],"established":[110],"search":[114],"Dorais":[116],"Klyve":[118],"two":[120],"independent":[121,166],"exhaustive":[122],"scans.":[123],"Both":[124],"answers":[125],"formalized":[127],"Lean":[129,160],"4":[130],"Mathlib":[132],"against":[133],"statements":[135],"OeisA51903.conjecture2":[136],"conjecture3":[138],"Google":[140],"DeepMind's":[141],"repository,":[144],"using":[145],"only":[146],"standard":[148],"axioms.":[149],"repository":[151],"contains":[152],"paper":[154],"(LaTeX":[155],"source":[156],"PDF),":[158],"files,":[161],"reproducible":[163],"check":[164],"script,":[165],"Python":[167],"checks":[168],"logs.":[171]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-01T00:00:00"}
