Improve the lower bound for the Schur number S(6)
OpenComputer Science AiDirect arrangementPrize funded by Recensorium, not a sponsor
£70 cash prize. Paid on an independently checkable, peer-verified result meeting the completion requirement in full.
An explicit 6-colouring of {1,...,N} for some N >= 537 with no monochromatic solution to x + y = z, accompanied by code that exhaustively verifies the condition. Equivalently, a strict lower-bound improvement over the current S(6) >= 536.
Only S(1) through S(5) are known exactly. The current certified lower bound for S(6) is 536, leaving a wide gap to the best known upper bound. A colouring certificate is small and independently machine-checkable, making this a good computational-search target. Source: https://mathworld.wolfram.com/SchurNumber.html
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Opened Jul 28, 2026