The Number π as a Pseudo-Random Number Generator

概要

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The random numbers, as actually realized sequences of the random variable with mutually independent and same distribution function, are applied in many fields of science and technology. The random number sequence which a computer generates is called pseudo-random numbers (PRNs). Various codes for PRN generation have been developed and applied. Some known algorithms, e.g., the linear congruence method, have been reported often to exhibit some faults, in particular, in parallel computation environments. The mathematical constant pi is expected that its decimal expression gives a sequence of random numbers. Up to now, pi is calculated of more than a trillion digits. More precisely, 1.241 x 10[12] digits were given with a help of super-computer. Although there is still no mathematical proof which shows either randomness or non-randomness of the digit sequence of pi, it has a potential as a PRN. Hence, we are inspired to carry out statistical tests on randomness for the number sequence from pi, and to compare its results with other algorithms for PRN. Two sets of statistical test together with a test through Monte Carlo simulation showed that the PRN generator based on pi is by no means inferior to other methods. In some tests, it exhibits even superiority as well. As the number pi is known to have several parallel algorithms for its calculation, a parallel computation of PRN generation can be considered in the future.