In this paper we present two new algorithms, called Queen Search 2 (QS2) and Queen Search 3 (QS3). QS2 and QS3 are probabilistic local search algorithms, based on a gradient-based heuristic. These algorithms, running in almost linear time, are capable of finding a solution for extremely large size n-queens problems. For example, QS3 can find a solution for 500,000 queens in approximately one and a half minutes.