{"id":"https://openalex.org/W7225416561","doi":"https://doi.org/10.6084/m9.figshare.34933848","title":"\u57fa\u4e8e\u53cc\u884c\u7f51\u683c\u4e0e\u53cd\u8bc1\u6982\u7387\u6cd5\uff0c\u63a2\u7a76\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3Investigating the Goldbach Conjecture Based on the Double-Row Grid and the Proof-by-Contradiction Probability Method","display_name":"\u57fa\u4e8e\u53cc\u884c\u7f51\u683c\u4e0e\u53cd\u8bc1\u6982\u7387\u6cd5\uff0c\u63a2\u7a76\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3Investigating the Goldbach Conjecture Based on the Double-Row Grid and the Proof-by-Contradiction Probability Method","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225416561","doi":"https://doi.org/10.6084/m9.figshare.34933848"},"language":"en","primary_location":{"id":"doi:10.6084/m9.figshare.34933848","doi":"https://doi.org/10.6084/m9.figshare.34933848","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34933848","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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/10.6084/m9.figshare.34933848","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148320962","display_name":"Yunzhi Tian","orcid":"https://orcid.org/0009-0000-0632-2025","observed_orcids":["https://orcid.org/0009-0000-0632-2025"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yunzhi Tian","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-0632-2025","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148320962"],"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":1.0,"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":1.0,"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/T13500","display_name":"Probability and Statistical Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/goldbach-conjecture","display_name":"Goldbach conjecture","score":0.996999979019165},{"id":"https://openalex.org/keywords/kolmogorov-axioms","display_name":"Kolmogorov axioms","score":0.7900000214576721},{"id":"https://openalex.org/keywords/law-of-excluded-middle","display_name":"law of excluded middle","score":0.8999999761581421},{"id":"https://openalex.org/keywords/prime-number-distribution","display_name":"prime number distribution","score":0.375}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8234000205993652},{"id":"https://openalex.org/C143732363","wikidata":"https://www.wikidata.org/wiki/Q485520","display_name":"Goldbach's conjecture","level":3,"score":0.8062999844551086},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7982000112533569},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6413999795913696},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5562000274658203},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5249999761581421},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46459999680519104},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3813000023365021},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C167927819","wikidata":"https://www.wikidata.org/wiki/Q1930567","display_name":"Shuffling","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.29670000076293945},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C73038302","wikidata":"https://www.wikidata.org/wiki/Q1466519","display_name":"Geometry of numbers","level":3,"score":0.2721000015735626},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2605000138282776}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.6084/m9.figshare.34933848","doi":"https://doi.org/10.6084/m9.figshare.34933848","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34933848","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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:10.6084/m9.figshare.34933848.v1","doi":"https://doi.org/10.6084/m9.figshare.34933848.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34933848.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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:10.6084/m9.figshare.34933848","doi":"https://doi.org/10.6084/m9.figshare.34933848","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34933848","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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/W7225108440","https://openalex.org/W7159576191","https://openalex.org/W7202271088","https://openalex.org/W7162184926","https://openalex.org/W7224761273","https://openalex.org/W7196929932","https://openalex.org/W7212370273","https://openalex.org/W4416285858","https://openalex.org/W7213286437","https://openalex.org/W6903763197"],"abstract_inverted_index":{"This":[0],"paper":[1,69],"constructs":[2],"a":[3,9,18,65,87,103,109,128,142,167,170,190,207],"double-row":[4],"odd-number":[5],"spatial":[6],"model":[7,89],"with":[8,45,93],"constant":[10],"column":[11,54,77,105],"sum":[12,27,47,78],"to":[13,114,198],"investigate":[14],"the":[15,26,46,49,52,60,71,76,82,100,118,124,134,152,161,186,202,212,229,232],"Goldbach":[16,213],"Conjecture:":[17],"large":[19],"even":[20],"number":[21],"2m":[22,138],"is":[23,95,112,131,149,165,169,192,226],"decomposed":[24],"into":[25],"of":[28,48,62,90,123,144,189,204,219,231],"two":[29],"odd":[30,35],"numbers,":[31],"and":[32,41,80,84,117,147,201,211],"all":[33],"such":[34],"numbers":[36,50],"are":[37],"arranged":[38],"in":[39,51,64],"ascending":[40],"descending":[42],"order":[43],"respectively,":[44],"same":[53],"equaling":[55],"2m.":[56],"Letting":[57],"p":[58],"denote":[59],"proportion":[61],"primes":[63],"single":[66,104],"row,":[67],"this":[68,98,220],"adopts":[70],"relaxation":[72],"method:":[73],"by":[74],"removing":[75],"constraint":[79],"shuffling":[81],"upper":[83],"lower":[85],"rows,":[86],"relaxed":[88],"\"independent":[91],"sampling":[92],"replacement\"":[94],"established.":[96],"In":[97],"model,":[99],"probability":[101,120,143,177,188],"that":[102,121,151,185],"does":[106],"not":[107],"contain":[108,127],"prime":[110,129],"pair":[111,130],"derived":[113],"be":[115],"1\u2212p\u00b2,":[116],"total":[119],"none":[122],"m\u22122":[125],"columns":[126],"(1\u2212p\u00b2)^(m\u22122).":[132],"Substituting":[133],"computational":[135],"verification":[136],"bound":[137],"=":[139,234],"4\u00d710\u00b9\u2078":[140],"yields":[141],"approximately":[145],"10^(\u22121.88\u00d710\u00b9\u2075),":[146],"it":[148,174],"proven":[150],"limit":[153],"approaches":[154],"0":[155],"as":[156],"m\u2192\u221e.":[157],"Based":[158],"on":[159],"this,":[160],"\"Proof-by-Contradiction":[162],"Probability":[163],"Method\"":[164],"proposed:":[166],"counterexample":[168,191,208],"deterministic":[171,224],"event;":[172],"if":[173],"exists,":[175],"its":[176],"must":[178],"equal":[179],"1.":[180,196],"The":[181,216],"above":[182],"derivation":[183],"demonstrates":[184],"survival":[187],"strictly":[193],"less":[194],"than":[195],"According":[197],"Kolmogorov's":[199],"axioms":[200],"Law":[203],"Excluded":[205],"Middle,":[206],"cannot":[209],"exist,":[210],"Conjecture":[214],"holds.":[215],"generalization":[217],"significance":[218],"method":[221],"for":[222],"determining":[223],"propositions":[225],"discussed":[227],"at":[228],"end":[230],"paper.\u672c\u6587\u9488\u5bf9\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u6784\u5efa\u6bcf\u5217\u548c\u6052\u5b9a\u7684\u53cc\u884c\u5947\u6570\u7a7a\u95f4\u6a21\u578b\uff1a\u5c06\u5927\u5076\u65702m\u62c6\u6210\u4e24\u4e2a\u5947\u6570\u4e4b\u548c\uff0c\u628a\u6240\u6709\u8fd9\u6837\u7684\u5947\u6570\u5206\u522b\u6309\u5347\u5e8f\u3001\u964d\u5e8f\u6392\u5217\uff0c\u540c\u5217\u76f8\u52a0\u4e3a2m\u3002\u8bb0\u5355\u884c\u7d20\u6570\u5360\u6bd4\u4e3ap\u3002\u672c\u6587\u91c7\u7528\u653e\u7f29\u6cd5\uff1a\u89e3\u9664\u5217\u548c\u7ea6\u675f\u3001\u6253\u4e71\u4e0a\u4e0b\u884c\u6392\u5217\uff0c\u5728\"\u6709\u653e\u56de\u3001\u72ec\u7acb\u62bd\u53d6\"\u7684\u5bbd\u677e\u6a21\u578b\u4e2d\u63a8\u5f97\u5355\u5217\u4e0d\u51fa\u73b0\u7d20\u6570\u5bf9\u7684\u6982\u7387\u4e3a1\u2212p\u00b2\uff0cm\u22122\u5217\u5168\u90e8\u4e0d\u51fa\u73b0\u7684\u603b\u6982\u7387\u4e3a(1\u2212p\u00b2)^(m\u22122)\uff1b\u4ee3\u5165\u9a8c\u8bc1\u8fb9\u754c2m":[233],"4\u00d710\u00b9\u2078\u5f97\u8be5\u6982\u7387\u7ea6\u4e3a10^(\u22121.88\u00d710\u00b9\u2075)\uff0c\u5e76\u8bc1\u5f97m\u2192\u221e\u65f6\u5176\u6781\u9650\u4e3a0\u3002\u636e\u6b64\u63d0\u51fa\"\u53cd\u8bc1\u6982\u7387\u6cd5\"\uff1a\u53cd\u4f8b\u662f\u786e\u5b9a\u6027\u4e8b\u4ef6\uff0c\u82e5\u5b58\u5728\u5219\u5176\u6982\u7387\u5fc5\u987b\u7b49\u4e8e1\uff1b\u800c\u4e0a\u8ff0\u63a8\u5bfc\u8868\u660e\u53cd\u4f8b\u5b58\u6d3b\u6982\u7387\u4e25\u683c\u5c0f\u4e8e1\uff0c\u4f9d\u636e\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u516c\u7406\u4e0e\u6392\u4e2d\u5f8b\uff0c\u53cd\u4f8b\u4e0d\u5b58\u5728\uff0c\u54e5\u5fb7\u5df4\u8d6b\u731c\u60f3\u6210\u7acb\u3002\u6587\u672b\u8ba8\u8bba\u4e86\u8be5\u65b9\u6cd5\u5bf9\u786e\u5b9a\u6027\u547d\u9898\u5224\u5b9a\u7684\u63a8\u5e7f\u610f\u4e49\u3002":[235]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}