Van der Waerden number $W(6,5)$
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 $5$.
Lower bound:
$98755$
(98,755)
Upper bound:
Unknown
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
- Lower bound: None yet
- Upper bound: None yet
Updates from the literature
-
2012-06-06
Lower bound: $98741$
(98,741)
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] -
2016-11
Lower bound: $98755$
(98,755)
Komkov, M. (2016). viXra:1611.0385.
[via Monroe, D. (2019). New Lower Bounds for van der Waerden Numbers Using Distributed Computing. arXiv preprint arXiv:1603.03301v6.]