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Happy Friday the 13th

When a common year of 365 days starts on a Sunday, as it did this year, 2 Friday the 13ths are inevitable. The 1st one was in January and the 2nd in October.

Image via Kelli Marshall

Image via Kelli Marshall

October 13, 2017 is a Friday, ushering the second of two Friday the 13ths in 2017. Any calendar year has at least one Friday the 13th, but no more than three Friday the 13ths. The last time we had only one Friday the 13th in a calendar year was in May 2016 and the next time won’t be until August 2021. Three Friday the 13ths last took place in 2015 (February, March, November), and will next happen in 2026. This year, in 2017, there are two Friday the 13ths (January and October).

Not that we at EarthSky suffer from friggatriskaidekaphobia – an irrational fear of Friday the 13th – but, gosh darn, this year’s second Friday the 13th on October 13, 2017, happens exactly 39 weeks (3 x 13 weeks) after the last Friday the 13th in Janaury 2017. But that’s hardly the end of it. Next year, in 2018 (which also has two Friday the 13ths), the first of the two comes on April 13, 2018, exactly 26 weeks (2 x 13 weeks) after the Friday the 13th in October 2017. Then the second Friday the 13th of 2018 falls on July 13, 2018, exactly 13 weeks after the first Friday the 13th in April 2018.

Yikes, that’s quite a few of coincidences involving the number 13 … though we could cite many more!

Follow the links below to learn more about why some people fear this day and about the intriguing mathematics of Friday the 13th and the calendar.

Scary coincidence or super unlucky?

In 2017, blame a common year starting on Sunday

How often do January-October Friday the 13ths happen?

Rhyme and reason for the 400-year Friday the 13th cycle

Gregoriana cycle of 372 years

Can a leap year start on Sunday?

Gioachino Rossini, a 19th century Italian composer. Folklorists say there's no written evidence that Friday the 13th was considered unlucky before the 19th century. The earliest known documented reference in English appears to be in Henry Sutherland Edwards' 1869 biography of Rossini.

Scary coincidence or super unlucky? Neither. It’s just a quirk of our calendar, as you’ll see as you keep reading.

The fact is that, according to folklorists, there’s no written evidence that Friday the 13th was considered unlucky before the 19th century. The earliest known documented reference in English appears to be in Henry Sutherland Edwards’ 1869 biography of Gioachino Rossini. His portrait is on this page. He doesn’t look scary.

Friday has always gotten a bad rap. In the Middle Ages, people would not marry – or set out on a journey – on a Friday.

There are also some links between Christianity and an ill association with either Fridays or the number 13. Jesus was said to be crucified on a Friday. Seating 13 people at a table was seen as bad luck because Judas Iscariot, the disciple who betrayed Jesus, is said to have been the 13th guest at the Last Supper. Meanwhile, our word for Friday comes from Frigga, an ancient Scandinavian fertility and love goddess. Christians called Frigga a witch and Friday the witches’ Sabbath.

In modern times, the slasher-movie franchise Friday the 13th has helped keep friggatriskaidekaphobia alive.

Best New Year’s gift ever! EarthSky moon calendar for 2017

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The Friday the 13th slasher-movie franchise helped keep this day maintain its notoriety.  Image via Wikimedia Commons

The Friday the 13th slasher-movie franchise helped keep this day maintain its notoriety. Image via Wikimedia Commons

In 2017, blame a common year starting on Sunday. Whenever a common year of 365 days starts on a Sunday, it’s inevitable that the months of January and October will start on a Sunday. And any month starting on a Sunday always has a Friday the 13th. So this year, in 2017, we’ll have a Friday the 13th in January and October.

The last time a common year started on a Sunday was 11 years ago, in the year 2006. The next time will be six years from 2017, in 2023. Some of you may wonder if there’s some formula that governs how this twofold Friday the 13th drama repeats itself. The answer is a definite yes. Keep in mind that this January-October Friday the 13th year can only happen in a common year of 365 days, and when January 1 falls on a Sunday.

Any calendar year that happens one year after a leap year will recur in 6, 17 and 28 years. Therefore, if our twofold Friday the 13th year comes one year after a leap year, as it does in 2017, the days and dates will match up again in 6, 17 and 28 years. Therefore, the years 2023, 2034 and 2045 will all harbor January and October Friday the 13ths:

2017 + 6 = 2023

2017 + 17 = 2034

2017 + 28 = 2045

Calendar for 2017

Calendar for 2017 via TimeandDate.com.

How often do January-October Friday the 13ths happen? More often than you might imagine! The first January-October Friday the 13th year in the 21st century (2001 to 2100) occurred in 2006, which is two years after a leap year. Any calendar year happening two years after a leap year will have days and dates matching up again in periods of 11, 17 and 28 years:

2006 + 11 = 2017

2006 + 17 = 2023

2006 + 28 = 2034

We continue the cycle onward to find a grand total of 10 January-October Friday the 13th years for the 21st century (2001 to 2100):

2006, 2017, 2023, 2034, 2045, 2051, 2062, 2073, 2079 and 2090

Because the year 2090 is two years after a leap year, we might be tempted to project the next January-October Friday the 13th to the year 2101:

2090 + 11 = 2101

Alas, here’s where the Gregorian calendar throws a monkey wrench at us. By Gregorian calendar rules, century years not equally divisible by 400 (e.g. 2100, 2200, 2300) are not leap years of 366 days – but rather, common years of 365 days. So the suppression of the leap year in 2100 perturbs the cycle, bringing about the first January-October Friday the 13th year of the 22nd century (2101 to 2200) in the year 2102, instead of 2101.

By good fortune, we can pretend that the year 2102 comes two years after a leap year, to project the recurrence of January-October Friday the 13th years in periods of 11, 17 and 28 years.

2102 + 11 = 2113

2102 + 17 = 2119

2102 + 28 = 2130

We continue the cycle onward to find a total of 11 January-October Friday the 13th years for the 22nd century (2100 to 2200):

2102, 2113, 2119, 2130, 2141, 2147, 2158, 2169, 2175, 2186 and 2192

In the 23rd century (2201 to 2300), the cycle is perturbed again. The first January-October Friday the 13th year does not fall in 2203 – but rather in 2209, which is one year after a leap year. Any calendar year happening one year after a leap year recurs in 6, 17 and 28 years.

Thus, we find 11 January-October Friday the 13th years for the 23rd century (2201 to 2300):

2209, 2215, 2226, 2237, 2243, 2254, 2265, 2271, 2282, 2293 and 2299

In the 24th century (2301 to 2400), the cycle is again perturbed. The first January-October Friday the 13th year does not come in 2310 – but rather in 2305, or one year after a leap year. That gives 11 January-October Friday the 13th years for the 24th century (2301 to 2400):

2305, 2311, 2322, 2333, 2239, 2350, 2361, 2367, 2378, 2389 and 2395

Because the year 2400 IS a leap year of 366 days, the cycle is NOT perturbed in the following 25th century (2401 to 2500). So we can keep on going to find 10 January-October Friday the 13th years for the 25th century (2401 to 2500).

2406, 2417, 2423, 2434, 2445, 2451, 2462, 2473, 2479 and 2490

Statistically speaking … the modal day for the 13th to occur on is Friday, with 688 occurrences in the 4,800-month cycle. (Of course, this is the same graph for the 6th as well as the 13th, 20th and 27th.) Caption and graphic via datagenetics.com.

Rhyme and reason for the 400-year Friday the 13th cycle.

Because the Gregorian calendar has a 400-year cycle, the January-October Friday the 13th years recur in cycles of 400 years. For example, respective January-October Friday the 13th calendar years are exactly 400 years apart in the 21st and 25th centuries:

21st century (2001 to 2100):

2006, 2017, 2023, 2034, 2045, 2051, 2062, 2073, 2079 and 2090

25th century (2401 to 2500):

2406, 2417, 2423, 2434, 2445, 2451, 2462, 2473, 2479 and 2490

Gregoriana cycle of 372 years.

It appears as though cycles of 372 and 400 years (372 + 28) prevail over the long course of centuries. Take the year 2017, for instance:

2017 + 372 = 2389

2017 + 400 = 2417

The 372-year period is known as the Gregoriana eclipse cycle, which we elaborate about in our post: How often does a solar eclipse happen on the March equinox?

As magical as all of this Friday the 13th calendar intrigue appears to be, it’s not supernatural. It’s entertaining number play, even if it may haunt our uncomprehending minds.

Can a leap year start on Sunday?

Yes, a leap year of 366 days can start on a Sunday. It last occurred in the year 2012 and will next happen in 2040. Any leap year starting on a Sunday has three Friday the 13ths which fall in January, April and July. The days and dates of any leap year match up again in periods of 28 years. So we have only four January-April-July Friday the 13th years in the 21st century (2001 to 2100):

2012, 2040, 2068 and 2096

… and whether or not it is clear to you, the universe is unfolding as it should. Resin, acrylic paint and archival print on transparency on panel, by Boston artist Jessica Dunegan.

Bottom line: Scared of Friday the 13th? It’s just a feature of our Gregorian calendar, and a pretty common one at that. From what we’ve been able to gather, the 400-year cycle displayed by the Gregorian calendar features 688 Friday the 13ths. We find that 43 of these 400 years harbor January-October Friday the 13ths, accounting for 86 of the 688 Friday the 13ths in one 400-year cycle.

2015 had 3 Friday the 13ths. What are the odds?

When does Friday the 13th have a full moon?

Bruce McClure

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