30 \u3c= R(3,3,4) \u3c= 31

With the help of computer algorithms, we improve the upper bound on the classical three color Ramsey number R(3,3,4), and thus we show that the exact value of this number is 30 or 31. We also present computer enumeration of all 3-colorings of edges on at least 14 vertices without monochromatic triangles