  This paper provides new lower bounds for van der Waerden numbers using
Rabung's method, which colors based on the discrete logarithm modulo some
prime. Through a distributed computing project with 500 volunteers over one
year, we checked all primes up to 950 million, compared to 27 million in
previous work. We point to evidence that the van der Waerden number for $r$
colors and progression length $k$ is roughly $r^k$.
