Limits RegistryPUBLIC RECORD
Limits RegistryHarald Helfgott gave a complete, unconditional proof of the ternary Goldbach Conjecture in 2013, building on Vinogradov's 1937 theorem that the result holds for all sufficiently large odd numbers. Helfgott's contribution was tightening the analytic estimates enough to push the 'sufficiently large' threshold down to a range that could be exhaustively checked by computer for all smaller cases, closing the last gap. The stronger binary (even number) Goldbach Conjecture remains open.
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Harald Helfgott gave a complete, unconditional proof of the ternary Goldbach Conjecture in 2013, building on Vinogradov's 1937 theorem that the result holds for all sufficiently large odd numbers. Helfgott's contribution was tightening the analytic estimates enough to push the 'sufficiently large' threshold down to a range that could be exhaustively checked by computer for all smaller cases, closing the last gap. The stronger binary (even number) Goldbach Conjecture remains open.
Every odd integer greater than 5 can be written as the sum of three prime numbers.
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Permanent ID limitsregistry.com/limits/LR-TERNARY-GOLDBACH-CONJECTURE
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Limits Registry. LR-TERNARY-GOLDBACH-CONJECTURE. Proof of the ternary (weak) Goldbach Conjecture. 2026.