Schur Numbers and the Ramsey Numbers N(3, 3, ..., 3; 2)

Listed below is a partition of the integers l-157, found by a backtrack search technique, into five sum-free sets (i, j E S 3 i + j $ S). This improves lower bounds on the fifth Schur number, ~(5) > 157, and all subsequent Schur numbers, s(k) > ~(315)~/~ for k > 5, [I]. Also this improves the lower bound on the Ramsey number N(3,3,3,3,3; 2) > 158 and all subsequent Ramsey numbers N(3, 3 ,..., 3; 2) [2].