Van der Waerden number $W(6,11)$
The smallest number $n$ such that if the integers $1$ to $n$ are colored with $6$ colors, there must be a monochromatic arithmetic progression of length $11$.
Lower bound:
$419188538044$
(419,188,538,044)
Upper bound:
Unknown
Updates
-
2018-03
Lower bound: $39840917502$
(39,840,917,502)
Blankenship, T., Cummings, J., & Taranchuk, V. (2018). A new lower bound for van der Waerden numbers. European Journal of Combinatorics, 69, 163-168. -
2019-05-22
Lower bound: $419188538044$
(419,188,538,044)
Monroe, D. (2019). New Lower Bounds for van der Waerden Numbers Using Distributed Computing. arXiv preprint arXiv:1603.03301v6.
[via Van der Waerden number - Wikipedia]