Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. A new algorithm called Mersenne twister (MT) is proposed for generating uniform pseudorandom numbers. For a particular choice of parameters, the algorithm provides a super astronomical period of 2 19937 -1 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. This is a new variant of the previously proposed generators, TGFSR, modified so as to admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution up to v bits accuracy for 1≤v≤32 is also shown to be good. An algorithm is also given that checks the primitivity of the characteristic polynomial of MT with computational complexity O(p 2 ) where p is the degree of the polynomial. We implemented this generator in portable C-code. It passed several stringent statistical tests, including diehard. Its speed is comparable to other modern generators. Its merits are due to the efficient algorithms that are unique to polynomial calculations over the two-element field. (Source:

References in zbMATH (referenced in 338 articles , 2 standard articles )

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  1. Harase, Shin: A table of short-period Tausworthe generators for Markov chain quasi-Monte Carlo (2021)
  2. Belov, A. A.; Kalitkin, N. N.; Tintul, M. A.: Unreliability of available pseudorandom number generators (2020)
  3. Ferone, Daniele; Festa, Paola; Guerriero, Francesca: An efficient exact approach for the constrained shortest path tour problem (2020)
  4. Gevorkyan, M. N.; Demidova, A. V.; Korol’kova, A. V.; Kulyabov, D. S.: A practical approach to testing random number generators in computer algebra systems (2020)
  5. Gevorkyan, M. N.; Korolkova, A. V.; Kulyabov, D. S.; Sevast’yanov, L. A.: A modular extension for a computer algebra system (2020)
  6. Leövey, H.; Römisch, W.: Randomized QMC methods for mixed-integer two-stage stochastic programs with application to electricity optimization (2020)
  7. Schippers, Michael; Koscholke, Jakob: A general framework for probabilistic measures of coherence (2020)
  8. Bhattacharjee, Kamalika; Das, Sukanta: Random number generation using decimal cellular automata (2019)
  9. Camassa, Roberto; Kilic, Zeliha; McLaughlin, Richard M.: On the symmetry properties of a random passive scalar with and without boundaries, and their connection between hot and cold states (2019)
  10. Choi, Jeong-Ok; Yu, Unjong: Newman-Ziff algorithm for the bootstrap percolation: application to the Archimedean lattices (2019)
  11. Dos Reis, Daniel Morais; Goulart, Natã; Noronha, Thiago F.; De Souza, Sérgio Ricardo: On the problem of minimizing the cost with optical devices in wavelength division multiplexing optical networks: complexity analysis, mathematical formulation and improved heuristics (2019)
  12. Hagebring, Fredrik; Lennartson, Bengt: Time-optimal control of large-scale systems of systems using compositional optimization (2019)
  13. Harase, Shin: Comparison of Sobol’ sequences in financial applications (2019)
  14. Harase, Shin: Conversion of mersenne twister to double-precision floating-point numbers (2019)
  15. Járai, Antal A.; Sun, Minwei: Toppling and height probabilities in sandpiles (2019)
  16. Kolonko, Michael; Gu, Feng; Wu, Zijun: Improving the statistical quality of random number generators by applying a simple ratio transformation (2019)
  17. Kuschel, Torben; Bock, Stefan: Solving the weighted capacitated planned maintenance problem and its variants (2019)
  18. Porretta, Luciano; Catanzaro, Daniele; Halldórsson, Bjarni V.; Fortz, Bernard: A \textitbranch& \textitpricealgorithm for the minimum cost clique cover problem in max-point tolerance graphs (2019)
  19. Terenin, Alexander; Dong, Shawfeng; Draper, David: GPU-accelerated Gibbs sampling: a case study of the horseshoe probit model (2019)
  20. Yaegashi, Yuta; Yoshioka, Hidekazu; Tsugihashi, Kentaro; Fujihara, Masayuki: Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process (2019)

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