A sum-free 7-colouring of {1, ..., 1698}: S(7) >= 1698 and R_7(3) >= 1700

A 7-colouring of {1, ..., 1698} in which no colour class contains x, y and x + y (x = y allowed), showing that the Schur number S(7) is at least 1698. The previous best lower bound is S(7) >= 1696 (F. Rowley, arXiv:2107.03560, 2021; OEIS A045652), which improved S(7) >= 1680 (Fredricksen and Sweet, 2000). We found no larger published value up to 2026-10-26. Since a sum-free k-colouring of {1, ..., n} gives a k-colouring of the edges of K_{n+1} with no monochromatic triangle, the colouring also gives the multicolour Ramsey bound R_7(3) >= 1700 (Radziszowski's survey DS1, revision 18, lists 1698). The colouring is symmetric, c(x) = c(1699 - x), and was found by local search seeded from Rowley's 1696 colouring. The archive contains the colouring and a standard-library Python script that checks every pair. Searches and verification were carried out with Claude (Anthropic) under the direction of Kerem Özdemir.