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 $r^k$.

翻译：本文使用Rabung 的方法为van der Waerden 数字提供了新的下限,该方法的颜色以离散对数模数为主,一年中有500名志愿者参与的分布式计算项目,我们检查了高达9.5亿的百分数,而以前的工作为2 700万。我们指出,凡德瓦尔登的彩色和递进长度为$($)和K($)的百分数大约是$(k)美元。