Van der Waerden number $W(3,10)$
The smallest number $n$ such that if the integers $1$ to $n$ are colored with $3$ colors, there must be a monochromatic arithmetic progression of length $10$.
Lower bound:
$4173725$
(4,173,725)
Upper bound:
Unknown
Updates
-
2012-06-06
Lower bound: $4173725$
(4,173,725)
Rabung, J., & Lotts, M. (2012). Improving the use of cyclic zippers in finding lower bounds for van der Waerden numbers. the electronic journal of combinatorics, P35-P35.
[via Van der Waerden number - Wikipedia]