# David Madore's WebLog: On days of the week in the Gregorian calendar

(Wednesday)

## On days of the week in the Gregorian calendar

Amaze your friends! Did you know that…

In the Gregorian (i.e. our present) calendar, the thirteenth of a month falls more frequently on a Friday than on any other day: 688 times on a Friday, 687 times on a Sunday or Wednesday, 685 times on a Monday or Tuesday, and 684 times on a Thursday or Saturday, all during a period of 400 years (the full cycle of the Gregorian calendar); on the other hand, January 1st falls more frequently on a Sunday, Tuesday or Friday (58 times each) than Wednesday or Thursday (57 times each) or Monday or Saturday (56 times each). In the Julian calendar, on the other hand, the cycle is 28 years long (1461 weeks), and the days of the week are evenly distributed over any date (such as the thirteenth of a month, or January 1st).

(Reminder: in the Julian calendar, leap years are those whose common era number is divisible by four; in the Gregorian calendar, an exception is made for years whose number is divisible by one hundred but not by four hundred, and they are not leap; so the Gregorian calendar substracts three days in 400 years from the Julian calendar, and in those 400 Gregorian years there are exactly 20871 weeks.)

(Some day, when I muster the courage to do so, I'll describe the Gregorian lunar calendar—which is another mess of complexity—and how it relates to the date of Easter.)

(Yeah, I know, nobody cares.) (And, no, I'm not that desperate for something to say.)