Delphi.science

A Schur 6-colouring of [1, 538]

Source: github.com/mysticflounder/schur-538/tree/c3306693e014961622…

Adam McKenna

Palomar Registrypalomar/PALOMAR-2026-11-04-000007Nov 4, 2026math.COscore 0

A Lean 4 check, with Lean core only, of the existence of a colouring of the integers 1 to 538 with 6 colours and no monochromatic x + y = z, with x = y allowed. So the integers 1 to 538 are the union of six sum-free sets, which gives S(6) ≥ 538 for the Schur number S(6). The largest lower bound in the sources that the author read on 3 November 2026 is S(6) ≥ 537, by Chen, Zhu and Long. The paper paper/schur-six-538.md in this repository states the result.

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