A sum-free 7-colouring of {1, ..., 1698}: S(7) >= 1698, R_7(3) >= 1700, S(12) >= 645388 and WS(10) >= 71340

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. Version 2 (2026-10-26) adds two consequences of S(7) >= 1698, each with an explicit colouring built from the 1698 colouring by the template inequalities of Ageron, Casteras, Pellerin, Portella, Rimmel and Tomasik (arXiv:2112.03175): S(12) >= 645388 (previously 644628) from S(n+5) >= 380 S(n) + 148, and WS(10) >= 71340 (previously 71256) for the weak Schur number from WS(n+3) >= 42 S(n) + 24. Both colourings come with a standard-library verifier. Version 2 also gives the author of arXiv:2107.03560 as F. Rowley (the version 1 README said D. Rowley), names the second check as a separate Claude session, and adds DOIs for the cited journal papers, citation metadata and a licence file. Searches and verification were carried out with Claude (Anthropic) under the direction of Kerem Özdemir.