The Gregorian calendar follows a pattern of leap years which repeats every 400 years. There are 4,800 months in 400 years, so the 13th of the month occurs 4,800 times in this interval. The number of times the 13th occurs on each weekday is given in the table below. As shown by Brown (1933), the thirteenth of the month is slightly more likely to be on a Friday than on any other day.

Day | Number of 13s | Fraction |

Sunday | 687 | 14.31% |

Monday | 685 | 14.27% |

Tuesday | 685 | 14.27% |

Wednesday | 687 | 14.31% |

Thursday | 684 | 14.25% |

Friday | 688 | 14.33% |

Saturday | 684 | 14.25% |

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.* New York: Dover, p. 27, 1987.

Brown, B. H. ``Solution to Problem E36.'' *Amer. Math. Monthly* **40**, 607, 1933.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
*Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England: Cambridge
University Press, pp. 14-15, 1992.

© 1996-9

1999-05-26