The Van der Waerden number W(r,k) is equal to the smallest N such that, if the numbers 1 through N are colored with r colors, there is always an arithmetic progression of length at least k with the same color.

Trivially, W(1,k) = k, W(r,1)=1, and W(r,2) = r+1 for all k,r. However, all other values are difficult to compute, and only 7 are known to date:

• W(2,3) = 9

• W(2,4) = 35

• W(2,5) = 178

• W(2,6) = 1132

• W(3,3) = 27

• W(3,4) = 293

• W(4,3) = 76

Will any other Van der Waerdin number be known by the end of 2030? This will be based on whenever the discovery is published, and the closure date is a year later than the deadline to ensure that I don't miss it if it is published right before 2030 ends.