Friday the Thirteenth: the Fearsome, the Common and the Unique

Jan 10, 2012
Jon Plotkin

: Another omen? - eschipul

Friday and 13: an unlucky number and an unlucky day; a double whammy when combined. How often does it happen? Is it really that bad? Can it be a palindrome?

It never bothered the ancients. But somehow, Friday the 13th is now a symbol of bad fortune, correlated with an uptick in suicides, automobile accidents, and absences from school. It also has some remarkable properties as a date, one of which is unique.

History of the Superstition

Some authorities claim that Friday the 13th's reputation as an omen of ill fortune begins with the persecution by King Philip the Fair of France (not to be confused with Philip the Handsome) of the Knights Templars on trumped-up charges. The date was October 13, 1307 -- a Friday. However, there is no evidence of the use in print of "Friday the 13th" until the 19th century. Most likely it simply evolved as an amalgam of two allegedly bad omens: the number thirteen and Friday.

Paraskavedekatriaphobia or Friggatriskaidekaphobia

Surveys show that fear of Friday the 13th afflicts about 8% of Americans. Some refuse even to get out of bed or eat. The evidence indicates that there may be more auto accidents or visits to emergency rooms, but there are a variety of other explanations than bad luck. Very likely the altered behavior of those with the above-named affliction (twice named, in fact; can you pronounce either one?) skews any data relating to occurrences on Friday the 13th.

Remarkable Properties of the Number Thirteen

Thirteen shows up in odd places. It is, for example, the number of cards in each suit in a standard deck of playing cards. There are 13 lunar cycles in a year, though the last one is fractional, and roughly 4 times 13 weeks in a year (we'll just throw away that pesky extra day). And of course there are 13 donuts in a baker's dozen.

13 is the smallest prime number of two or more different digits which is also a prime when the digits are reversed. And it is a Wilson Prime, of which there are only three below the number 400 billion.

How Common is Friday the Thirteenth?

There is at least one Friday the 13th in every calendar year; at most there are three. The maximum number occurs in 2012, then again in 2015. After that there won't be three Friday the 13ths in a single calendar year until 2026. Leap years with a Friday the 13th in January have three; non-leap years with one in February have three. If there is a Friday the 13th in May or June, then it is the only one that year.

By a strange mathematical quirk, the 13th day of any month is slightly more likely to fall on a Friday than any other day if you consider a period of several hundred years. Bad luck there, eh?

Friday the Thirteenth as a Palindromic Date

Back to more mundane matters, one might ask if there are any palindromic Friday the 13ths. In fact, one will ask. And one finds that in the years from AD 1 to AD 9,999, which comprise all the 8 digit dates when written mm/dd/yyyy, there is only one palindromic Friday the 13th. And that date is, drum roll please, 02/13/3120. That, of course, is in the American system. Europeans, who insist on expressing dates dd/mm/yyyy, get two, but they won't get their first until more than two millenia after the Yanks, on 13/05/5031. That'll teach 'em!