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The emergence of pseudo-random number generator (PRNG) has got rid of the difficulty of obtaining real random numbers, and PRNG has become the main method of generating random numbers in modern technology. Because of the wide application of random numbers, the quality of a PRNG has always been a concern, and the periodic characteristics of pseudo-random number sequences are the key to ensure their quality. In this paper, the value of π is computed by Monte Carlo method, and the error of the operation result is used to judge the periodicity of PRNG. We analyzed the nature of the Monte Carlo method for calculating the value of π; discussed the relationship between the number of random points and the calculating error; introduced the principle of evaluating the period characteristics of the pseudo-random number sequence, and analyzed the periodic characteristics of the five PRNGs through the experiment data and drew some interesting conclusions.