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weak-goldbach
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Vinogradov proved in 1937 that it holds for all sufficiently large odd numbers, but the threshold was astronomically large. Helfgott sharpened the circle method until the threshold fell to a range that a computer had already checked. It shows a common endgame: an asymptotic proof, then decades of bookkeeping to make its constants small.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 1742, from the Goldbach–Euler correspondence. Closed 2013, Harald Helfgott.