Van der Waerden number $W(4,8)$

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 $8$.

Lower bound: $12288156$ (12,288,156)
Upper bound: Unknown

Updates

Lower bound: $2388318$ (2,388,318)
Reference unknown
[via 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: $12288156$ (12,288,156)
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]