Goldbach Conjecture Proof

Goldbach Conjecture Proof | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Goldbach Conjecture Proof Daniel Thompson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2619839/v4 This work is licensed under a CC BY 4.0 License Status: Posted Version 4 posted You are reading this latest preprint version Show more versions Abstract The Goldbach conjecture was proposed by the German mathematician Christian Goldbach around the year 1742, to another well-known mathematician of that time Leonard Euler. The conjecture has been found to hold for all numbers up to 4 x 10⁸ but remains unproven until now. This paper proves the Goldbach conjecture by showing that elements of the addition of two odd prime numbers produce elements of the resulting even number. The resulting elements from the addition of two odd prime numbers evaluate to an equal amount thus proving that every even number can be expressed as the addition of two odd prime numbers. MSC: 11-xx. Number theory Twin Prime conjecture and Polignac’s conjecture Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 4 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2619839","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271416836,"identity":"a823f6f8-08ea-48b4-8549-2ca6259bdef2","order_by":0,"name":"Daniel Thompson","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Thompson","suffix":""}],"badges":[],"createdAt":"2023-02-23 09:44:26","currentVersionCode":4,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-2619839/v4","doiUrl":"https://doi.org/10.21203/rs.3.rs-2619839/v4","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52442338,"identity":"e425d1e3-4299-4fca-ad99-4e8e36a89341","added_by":"auto","created_at":"2024-03-11 17:21:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":167174,"visible":true,"origin":"","legend":"","description":"","filename":"GoldbachConjectureProofRIP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2619839/v4_covered_f8d4e2d0-1176-4598-8dd4-6c117198f8b6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Goldbach Conjecture Proof","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Number theory, Twin Prime conjecture and Polignac’s conjecture","lastPublishedDoi":"10.21203/rs.3.rs-2619839/v4","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2619839/v4","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Goldbach conjecture was proposed by the German mathematician Christian Goldbach around the year 1742, to another well-known mathematician of that time Leonard Euler. The conjecture has been found to hold for all numbers up to 4 x 10⁸ but remains unproven until now. This paper proves the Goldbach conjecture by showing that elements of the addition of two odd prime numbers produce elements of the resulting even number. 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