

The Gregorian calendar follows a pattern of leap years which repeats every 400 years. This is true since the number of days in 400 Gregorian years is

which is an exact number of weeks since it is divisible by 7 (namely, ). 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% On average, there are 1.72 ( ) Friday the 13ths per calendar year. The following table summarizes Friday the 13ths for years between 2000 and 2010. year months having Friday the 13th 2000 October 2001 April, July 2002 September, December 2003 June 2004 February, August 2005 May 2006 January, October 2007 April, July 2008 June 2009 February, March, November 2010 August The following Mathematica code can be used to generate the counts of the number of times a given weekday occurs. <<Miscellaneous`Calendar`; days={Monday,Tuesday,Wednesday,Thursday, Friday,Saturday,Sunday}; c=Count[Flatten[Table[DayOfWeek[{y,m,13}],{y,2000,2399}, {m,12}]],#]&/@days; TableForm[ {days,c,PaddedForm[#,{6,4}]&/@(100. c/Plus@@c), ToString//@Flatten[Position[Sort[c,Greater],#]]&/@c}, TableDirections->{Row,Column}, TableHeadings->{ {"day","numbers of 13s","percentage","rank"},None } ] Weekday





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. Parzen, E. Modern Probability Theory and Its Applications. New York: Wiley, pp. 26-27, 1960. 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.



© 1996-2007 Eric W. Weisstein