On the van der Waerden numbers w(2;3,t). ... Especially we introduce a novel (open-source) SAT solver, the tawSolver, which performs best on the SAT instances studied here, and which is actually the original DLL-solver by M. Davis et al. [Commun. ACM 5, 394–397 (1962; Zbl 0217.54002)], but with an efficient implementation and a modern heuristic typical for look-ahead solvers, applying the theory developed by the second author O. Kullmann [The OKlibrary: Introducing a “holistic” research platform for (generalised) SAT solving. Report CSR 1-2009. Report Series Computer Science Swansea University (2009)].