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The n-queens problem is a classical search
problem in the artificial intelligence (AI) area.
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.