The reliability of the tables containing Random Numbers (#RAN or RN) is checked. Two kinds of tests are proposed in order to check the reliability of series of $\lambda$-digit numbers obtained from a table of Random (one-digit) Numbers, where $\lambda = 1, 2, 3, 4$. The first test is based on the Central Limit Theorem and the Uniform Distribution Function of the involved Random Variables, and the second one is the $X^2$-test. A Random Numbers Table with 3500 digits is checked with very good results.