### Abstract

Two or more multiplicative congruential random-number generators with prime modulus combined by means of a method proposed by Wichmann and Hill yield a random-number generator equivalent to a multiplicative congruential random-number generator with modulus equal to the product of the moduli of the component multiplicative congruential generators. The period of a random-number sequence obtained by the Wichmann-Hill method is equal to the least common multiple of the periods of the combined sequences. One of the two purposes of this paper is to present a necessary and sufficient set of efficiently verifiable conditions, for the period to be equal to its maximum, which is the maximum of the least common multiple. Each of the conditions will be always satisfied or will be more easily verifiable, when the modulus of each of the component generators is safe prime. The other purpose is to derive an efficiently evaluatable formula for serial correlations of the maximum-period sequences by the Wichmann-Hill method. The authors recommend (i) to make the modulus of each of the component generators safe prime, and (ii) to chose the multipliers of the components so as to (a) maximize the period and (b) make the serial correlations small in absolute value.

Original language | English |
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Title of host publication | Winter Simulation Conference Proceedings |

Publisher | IEEE |

Pages | 309-315 |

Number of pages | 7 |

Publication status | Published - 1995 |

Event | Proceedings of the 1995 Winter Simulation Conference, WSC'95 - Arlington, VA, USA Duration: 1995 Dec 3 → 1995 Dec 6 |

### Other

Other | Proceedings of the 1995 Winter Simulation Conference, WSC'95 |
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City | Arlington, VA, USA |

Period | 95/12/3 → 95/12/6 |

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### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics
- Modelling and Simulation

### Cite this

*Winter Simulation Conference Proceedings*(pp. 309-315). IEEE.

**Combination of multiplicative congruential random-number generators with safe prime modulus.** / Sakamoto, Munetaka; Morito, Susumu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Winter Simulation Conference Proceedings.*IEEE, pp. 309-315, Proceedings of the 1995 Winter Simulation Conference, WSC'95, Arlington, VA, USA, 95/12/3.

}

TY - GEN

T1 - Combination of multiplicative congruential random-number generators with safe prime modulus

AU - Sakamoto, Munetaka

AU - Morito, Susumu

PY - 1995

Y1 - 1995

N2 - Two or more multiplicative congruential random-number generators with prime modulus combined by means of a method proposed by Wichmann and Hill yield a random-number generator equivalent to a multiplicative congruential random-number generator with modulus equal to the product of the moduli of the component multiplicative congruential generators. The period of a random-number sequence obtained by the Wichmann-Hill method is equal to the least common multiple of the periods of the combined sequences. One of the two purposes of this paper is to present a necessary and sufficient set of efficiently verifiable conditions, for the period to be equal to its maximum, which is the maximum of the least common multiple. Each of the conditions will be always satisfied or will be more easily verifiable, when the modulus of each of the component generators is safe prime. The other purpose is to derive an efficiently evaluatable formula for serial correlations of the maximum-period sequences by the Wichmann-Hill method. The authors recommend (i) to make the modulus of each of the component generators safe prime, and (ii) to chose the multipliers of the components so as to (a) maximize the period and (b) make the serial correlations small in absolute value.

AB - Two or more multiplicative congruential random-number generators with prime modulus combined by means of a method proposed by Wichmann and Hill yield a random-number generator equivalent to a multiplicative congruential random-number generator with modulus equal to the product of the moduli of the component multiplicative congruential generators. The period of a random-number sequence obtained by the Wichmann-Hill method is equal to the least common multiple of the periods of the combined sequences. One of the two purposes of this paper is to present a necessary and sufficient set of efficiently verifiable conditions, for the period to be equal to its maximum, which is the maximum of the least common multiple. Each of the conditions will be always satisfied or will be more easily verifiable, when the modulus of each of the component generators is safe prime. The other purpose is to derive an efficiently evaluatable formula for serial correlations of the maximum-period sequences by the Wichmann-Hill method. The authors recommend (i) to make the modulus of each of the component generators safe prime, and (ii) to chose the multipliers of the components so as to (a) maximize the period and (b) make the serial correlations small in absolute value.

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UR - http://www.scopus.com/inward/citedby.url?scp=0029482919&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029482919

SP - 309

EP - 315

BT - Winter Simulation Conference Proceedings

PB - IEEE

ER -