Friday the 13th

BMJ 1994; 308 doi: https://doi.org/10.1136/bmj.308.6939.1304b (Published 14 May 1994) Cite this as: BMJ 1994;308:1304
  1. S D Walter
  1. McMaster University Health Sciences Centre, Hamilton, Ontario, Canada L8N 3Z5.

    EDITOR, - C D O'Brien suggests that the 13th of a month is more likely to be a Friday than any other day,1 which has possible implications for the risk of transport accidents.2 O'Brien's calculations assume that the Gregorian calendar in current use has a cycle of exactly 400 years. This assumption is incorrect. In the Gregorian calendar leap days are added in years that are exactly divisible by 4 except for century years unless they are exactly divisible by 400 (thus, 2000 will be a leap year). Additionally, years that are evenly divisible by 4000 (for example, 8000 and 1600) are designated common years, when no leap day is added.3 I have calculated that 1 January 8000 will be a Saturday and that 1 January 16000 will be a Friday. Hence, rather than being 400 years the length of the Gregorian calendar cycle is 7x8000=56 000 years.

    The 13th of a month currently falls on a Friday 688 times per 400 years, the most of any day of the week; it occurs least often on Thursdays and Saturdays (only 684 times each).1 My calculations indicate that if we can hang on through the current period of bad luck the good times will return. Beginning in the year 8400, and continuing for the next 8000 years, the 13th will occur on a Friday - the minimum number of times - only 684 times per 400 years.

    The current Gregorian rules are sufficient to keep the calendar accurate to within one day per 20 000 years.3 I am not aware of what arrangements are in hand to add further leap day corrections at that point.


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