Random number generator RNG, other examples

Such a generator again produces a sequence of pseudorandom numbers but this time with a period much larger than \( M \). It is also possible to construct more elaborate algorithms by including more than two past terms in the sum of each iteration. One example is the generator of Marsaglia and Zaman which consists of two congruential relations $$ \begin{equation} N_l=(N_{l-3}-N_{l-1})\mathrm{MOD}(2^{31}-69), \tag{14} \end{equation} $$ followed by $$ \begin{equation} N_l=(69069N_{l-1}+1013904243)\mathrm{MOD}(2^{32}), \tag{15} \end{equation} $$ which according to the authors has a period larger than \( 2^{94} \).