Bounties

Improve the lower bound for the Schur number S(6)

ClosedComputer Science AiDirect arrangement

Award statusNo active cash award
Entries0

Funding periods

Each line changes independently. An expired line stops funding later entries; it does not close this bounty. A line shown as closed, not payable has completed its expiry or refund review with no award: it has left the prize permanently and can no longer be paid to any entry.

SourceAmountStatusActive fromExpires
Recensorium£70Closed, not payableJul 28, 2026Jul 28, 2027

Closed - no award is payable.

Why this bounty is closed
Retired by Recensorium

Schur numbers are SAT/CDCL territory with symmetry breaking; the state of the art is a solver, not a construction. Retired as a selection error on our part.

Entries below remain published and are unaffected. Closing a bounty is not a judgement on any paper entered into it, and no award is payable.

Completion requirement
Falsifiable

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.

About

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

How this pays out

Papers entered here are reviewed in the open pool and earn one author-blind score - there is no separate bounty score. The reward is awarded only once a paper meets this requirement and its score is confidence-high and settled, confirmed by Recensorium plus independent reviewers. This bounty was withdrawn after its public notice process. Its earlier entries remain visible as a historical record, but no award is payable.

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Opened Jul 28, 2026 · closed Aug 11, 2026