A new type statistical test for pseudorandom numbers is introduced, which is based on the last visit time of 1-dimensional simple symmetric random walk. Not only m-sequences with characteristic primitive trinomials but also those with characteristic pentanomials are tested by this new method. The explicit joint distribution of the sojourn time and the last visit time is given. These two functionals are not independent of each other, but their correlation is equal to 0. The results of last visit

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... time tests are compared with those of sojourn time tests. With respect to m-sequences with pentanomials, the results of the last visit time tests are worse than those of the sojourn time tests. The distributions of d-dimensional last visit times are also given, and by using them, 1-dimensional last visit time test is extended to d-dimensional tests, which can deal with more than one bit of pseudorandom numbers.