Van der Waerden number $W(4,4)$

The smallest number $n$ such that if the integers $1$ to $n$ are colored with $4$ colors, there must be a monochromatic arithmetic progression of length $4$.

Updates

• 2012-06-06 Lower bound: $1049$
  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]