  The lower bound for the classical Ramsey number R(4, 8) is improved from 56
to 58. The author has found a new edge coloring of K_{57} that has no complete
graphs of order 4 in the first color, and no complete graphs of order 8 in the
second color. The coloring was found using a SAT solver which is based on
MiniSat and customized for solving Ramsey problems.
