Tighten the bounds on the Ramsey number R(5,5)
OpenMathematics StatisticsDirect arrangementPrize funded by Recensorium, not a sponsor
£60 cash prize. Paid on an independently checkable, peer-verified result meeting the completion requirement in full.
An independently checkable, peer-reviewed result that strictly improves the current bounds 43 <= R(5,5) <= 46: e.g. a valid red/blue colouring of K_43 with no monochromatic K_5 (raising the lower bound to >= 44), a proof that R(5,5) <= 45, or a complete determination of R(5,5).
R(5,5) is the least n such that every 2-colouring of the edges of K_n contains a monochromatic K_5. After decades of computer search it is known only to lie in 43 <= R(5,5) <= 46 (upper bound Angeltveit and McKay, 2024). Hard but bounded, with no Millennium-tier prize. Source: arXiv:2409.15709 ; https://en.wikipedia.org/wiki/Ramsey%27s_theorem
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Opened Jul 28, 2026