SWhat changed
Every odd integer greater than five is a sum of three primes. Explicit major- and minor-arc estimates and an optimized large sieve cover all sufficiently large integers; a rigorously verified finite range overlaps that analytic threshold and completes the result.
Scientific scope
Every odd integer greater than five is a sum of three primes. Explicit major- and minor-arc estimates and an optimized large sieve cover all sufficiently large integers; a rigorously verified finite range overlaps that analytic threshold and completes the result. This is the three-primes theorem, not binary Goldbach for all even integers. Numerical verification alone is finite; global closure uses analytic estimates and their documented computational inputs. No assumption of the full Riemann or generalized Riemann hypothesis is introduced.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. This is the three-primes theorem, not binary Goldbach for all even integers. Numerical verification alone is finite; global closure uses analytic estimates and their documented computational inputs. No assumption of the full Riemann or generalized Riemann hypothesis is introduced.
Contributors
- The named authors in the research record · SCIENCE: Helfgott authors the analytic proof; Helfgott and Platt coauthor the finite verification. Source-specific roles remain in the native record. This is one theorem package, not a joint byline for both papers.
- The ternary Goldbach conjecture is true
- Numerical Verification of the Ternary Goldbach Conjecture up to8.875e30
Provisional WRS assessment, edition 2026-10-23.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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