Editing Friday the 13th (section)

== Occurrence ==

=== Distribution ===
Each 400&nbsp;year [[Gregorian calendar|Gregorian]] [[Solar cycle (calendar)|solar cycle]] contains 146,097&nbsp;days (with 97&nbsp;[[leap year|leap days]]) or exactly 20,871&nbsp;weeks. Each cycle contains the same pattern of days of the week and therefore the same pattern of Fridays that are on the 13th. The 13th&nbsp;day of the month is very slightly more likely to be a Friday than any other day of the week.<ref>{{cite news |author=Bodin, Magnus |date=13 November 1998 |title=About the date+day distribution along the epoch |website=x42 |url=http://x42.com/datelab/daydist.shtml |access-date=30 January 2014}}
</ref><ref>{{cite journal |first1=B.H. |last1=Brown |first2=Raphael |last2=Robinson |name-list-style=amp |year=1933 |title=Solution to problem E36 |journal=[[American Mathematical Monthly]] |volume=40 |issue=10 |page=607|doi=10.2307/2301694 |jstor=2301694 }}
</ref><ref>{{cite book |last=Meeus |first=J. |author-link=Jean Meeus |year=2007 |title=Mathematical Astronomy Morsels IV |page=367}}</ref>

:{| class=wikitable style="margin-left: auto; margin-right: auto; border: none;"
|+ Distribution of the 13th day per weekday over 4,800 months (400 years)
|- style="vertical-align:center; text-align:center"
! Day of the week
! Monday || Tuesday || Wednesday || Thursday || Friday || Saturday || Sunday
|- style="text-align:center;"
! Occurrences
| 685 || 685 || 687 || 684 || '''688''' || 684 || 687
|}

Any month that starts on a Sunday contains a Friday the 13th, and there is at least one Friday the 13th in every calendar year. 
The months with a Friday the 13th are determined by the [[Dominical letter]] (G, F, GF, etc.) of the year. Years which begin on the same day of the week and are of the same type (i.e. [[common year]] or [[leap year]]), will have a Friday the 13th in the same months.

This sequence, given here for 1900–2099, follows a 28-year cycle from 1&nbsp;March 1900 to 28&nbsp;February 2100:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Months with the 13th on a Friday for years from 1900 through 2100
|- style="vertical-align:center;"
! Years during which a Friday the 13th<br/>occurs in the month to the right<br/>(current and subsequent year are marked in bold)
! {{small|Month with<br/>its 13th on<br/>a Friday}}
! {{small|Year length<br/>and weekday of<br/>January the 1st}}
! {{small|Year's<br/>[[Dominical letter|dominical<br/>letter]]}}
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1905, 1911, 1922, 1928, 1933, 1939, 1950, 1956, 1961, 1967, 1978, 1984, 1989, 1995;<br/>{{grey|'''21st-century:'''}} 2006, 2012, 2017, 2023, 2034, 2040, 2045, 2051, 2062, 2068, 2073, 2079, 2090, 2096
| '''January'''
| [[Common year starting on Sunday|365: Sunday]]<br/>[[Leap year starting on Sunday|366: Sunday]]
| '''A'''<br/>'''A'''G
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1903, 1914, 1920, 1925, 1931, 1942, 1948, 1953, 1959, 1970, 1976, 1981, 1987, 1998;<br/>{{grey|'''21st-century:'''}} 2004, 2009, 2015, 2026, 2032, 2037, 2043, 2054, 2060, 2065, 2071, 2082, 2088, 2093, 2099
| '''February'''
| [[Common year starting on Thursday|365: Thursday]]<br/>[[Leap year starting on Thursday|366: Thursday]]
| '''D'''<br/>'''D'''C
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1903, 1908, 1914, 1925, 1931, 1936, 1942, 1953, 1959, 1964, 1970, 1981, 1987, 1992; 1998;<br/>{{grey|'''21st-century:'''}} 2009, 2015, 2020, 2026, 2037, 2043, 2048, 2054, 2065, 2071, 2076, 2082, 2093, 2099
| '''March'''
| [[Common year starting on Thursday|365: Thursday]]<br/>[[Leap year starting on Wednesday|366: Wednesday]]
| '''D'''<br/>E'''D'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1900, 1906, 1917, 1923, 1928, 1934, 1945, 1951, 1956, 1962, 1973, 1979, 1984; 1990;<br/>{{grey|'''21st-century:'''}} 2001, 2007, 2012, 2018, 2029, 2035, 2040, 2046, 2057, 2063, 2068, 2074, 2085, 2091, 2096
| '''April'''
| [[Common year starting on Monday|365: Monday]]<br/>[[Leap year starting on Sunday|366: Sunday]]
| '''G'''<br/>A'''G'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1904, 1910, 1921, 1927, 1932, 1938, 1949, 1955, 1960, 1966, 1977, 1983, 1988, 1994;<br/>{{grey|'''21st-century:'''}} 2005, 2011, 2016, 2022, 2033, 2039, 2044, 2050, 2061, 2067, 2072, 2078, 2089, 2095
| '''May'''
| [[Common year starting on Saturday|365: Saturday]]<br/>[[Leap year starting on Friday|366: Friday]]
| '''B'''<br/>C'''B'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1902, 1913, 1919, 1924, 1930, 1941, 1947, 1952, 1958, 1969, 1975, 1980, 1986, 1997;<br/>{{grey|'''21st-century:'''}} 2003, 2008, 2014, '''2025''', 2031, 2036, 2042, 2053, 2059, 2064, 2070, 2081, 2087, 2092, 2098
| '''June'''
| [[Common year starting on Wednesday|365: Wednesday]]<br/>[[Leap year starting on Tuesday|366: Tuesday]]
| '''E'''<br/>F'''E'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1900, 1906, 1917, 1923, 1928, 1934, 1945, 1951, 1956, 1962, 1973, 1979, 1984, 1990;<br/>{{grey|'''21st-century:'''}} 2001, 2007, 2012, 2018, 2029, 2035, 2040, 2046, 2057, 2063, 2068, 2074, 2085, 2091, 2096
| '''July'''
| [[Common year starting on Monday|365: Monday]]<br/>[[Leap year starting on Sunday|366: Sunday]]
| '''G'''<br/>A'''G'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1909, 1915, 1920, 1926, 1937, 1943, 1948, 1954, 1965, 1971, 1976, 1982, 1993, 1999;<br/>{{grey|'''21st-century:'''}} 2004, 2010, 2021, 2027, 2032, 2038, 2049, 2055, 2060, 2066, 2077, 2083, 2088, 2094, 2100
| '''August'''
| [[Common year starting on Friday|365: Friday]]<br/>[[Leap year starting on Thursday|366: Thursday]]
| '''C'''<br/>D'''C'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1901, 1907, 1912, 1918, 1929, 1935, 1940, 1946, 1957, 1963, 1968, 1974, 1985, 1991, 1996;<br/>{{grey|'''21st-century:'''}} 2002, 2013, 2019, 2024, 2030, 2041, 2047, 2052, 2058, 2069, 2075, 2080, 2086, 2097
| '''September'''
| [[Common year starting on Tuesday|365: Tuesday]]<br/>[[Leap year starting on Monday|366: Monday]]
| '''F'''<br/>G'''F'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1905, 1911, 1916, 1922, 1933, 1939, 1944, 1950, 1961, 1967, 1972, 1978, 1989, 1995,  2000;<br/>{{grey|'''21st-century:'''}} 2006, 2017, 2023, 2028, 2034, 2045, 2051, 2056, 2062, 2073, 2079, 2084, 2090
| '''October'''
| [[Common year starting on Sunday|365: Sunday]]<br/>[[Leap year starting on Saturday|366: Saturday]]
| '''A'''<br/>B'''A'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1903, 1908, 1914, 1925, 1931, 1936, 1942, 1953, 1959, 1964, 1970, 1981, 1987, 1992, 1998;<br/>{{grey|'''21st-century:'''}} 2009, 2015, 2020, 2026, 2037, 2043, 2048, 2054, 2065, 2071, 2076, 2082, 2093, 2099
| '''November'''
| [[Common year starting on Thursday|365: Thursday]] <br/> [[Leap year starting on Wednesday|366: Wednesday]]
|style="text-align:center"| '''D''' <br/>E'''D'''
|- style="text-align:center;" 
|style="text-align:left;"| {{grey|'''20th-century:'''}} 1901, 1907, 1912, 1918, 1929, 1935, 1940, 1946, 1957, 1963, 1968, 1974, 1985, 1991, 1996;<br/>{{grey|'''21st-century:'''}} 2002, 2013, 2019, 2024, 2030, 2041, 2047, 2052, 2058, 2069, 2075, 2080, 2086, 2097
| '''December'''
| [[Common year starting on Tuesday|365: Tuesday]]<br/>[[Leap year starting on Monday|366: Monday]]
| '''F'''<br/>G'''F'''
|}

=== Frequency ===
Although there is always at least one Friday the 13th per [[calendar year]], it can be as long as 14&nbsp;months between two Friday the 13ths.<ref>{{cite magazine |first=Solomon |last=Golomb |date=September 2007  |title=Solutions to 'Calendar oddities' |department=Golomb's Gambits |magazine=Johns Hopkins Magazine |volume=59 |issue=4 |url=http://pages.jh.edu/jhumag/0907web/golomb2.html}}</ref> The longest period that occurs without a Friday the 13th is 14&nbsp;months, either from July to September the following year being a [[common year starting on Tuesday]] [[Dominical letter|(F)]] (e.g. 2001–02, 2012–13 and 2018–19), or from August to October the following year being a [[leap year starting on Saturday]] [[Dominical letter|(BA)]] (e.g. 1999–2000 and 2027–28). The shortest period that occurs with a Friday the 13th is just one month, from February to March in a [[common year starting on Thursday]] [[Dominical letter|(D)]] (e.g. 2009, 2015 and 2026).

On average, there is a Friday the 13th once every 212.35&nbsp;days. Friday the 13ths occurs with an average frequency of 1.7218 per year or about 3477 since the year 1 CE.

==== Frequency within a single year ====
There can be no more than three Friday the 13ths in a single calendar year; either in February, March, and November in a [[common year starting on Thursday]] (such as 2009, 2015, or 2026) [[Dominical letter|(D)]], or January, April, and July in a [[leap year starting on Sunday]] (such as 1984, 2012, or 2040) [[Dominical letter|(AG)]].<ref name=Kher-13Facts-TaD>{{cite web |first=Aparna |last=Kher |title=13 Facts about Friday the 13th |website=Time and Date (timeanddate.com) |url=https://www.timeanddate.com/calendar/13-things-friday-13.html}}</ref>

In the 2000s, there were three Friday the 13ths in 2009, and two Friday the 13ths in 2001, 2002, 2006, and 2007. In the 2010s, there were three Friday the 13ths in 2012 and 2015, and two in 2013, 2017, 2018, and 2019.<ref name=Fri-13-months-days-TaD/> In the 2020s, there were two Friday the 13ths in 2020, 2023 and 2024. There will also be three Friday the 13ths in 2026, and two in 2029.<ref name=Fri-13-months-days-TaD/> The remaining years all have one Friday the 13th.<ref name=Fri-13-months-days-TaD/>

For the details see the table below; this table is for the Gregorian calendar and {{red|Jan}}/{{red|Feb}} for {{red|leap years}}:

:{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|- style="vertical-align:center; text-align:center"
! Year<br/>[[modular arithmetic|modulo]] 28 || {{red|1600 2000}} || 1700 2100 || 1800 2200 || 1900 2300 || Year<br/>[[modular arithmetic|modulo]] 28
|-
| {{red|00}} 06 {{figure space}}{{figure space}} 17 23 || Jan Oct || {{red|Feb}} Aug || Jun || {{red|Jan}} Apr Jul || {{red|00}} 06 {{figure space}}{{figure space}} 17 23
|-
| 01 07 {{red|12}} 18 {{figure space}}{{figure space}} || {{red|Jan}} Apr Jul || May || Feb Mar Nov || Sep Dec || 01 07 {{red|12}} 18 {{figure space}}{{figure space}}
|-
| 02 {{figure space}}{{figure space}} 13 19 {{red|24}} || Sep Dec || Jan Oct || {{red|Feb}} Aug || Jun || 02 {{figure space}}{{figure space}} 13 19 {{red|24}}
|-
| 03 {{red|08}} 14 {{figure space}}{{figure space}} 25 || Jun || {{red|Jan}} Apr Jul || May || Feb Mar Nov || 03 {{red|08}} 14 {{figure space}}{{figure space}} 25
|-
| {{figure space}}{{figure space}} 09 15 {{red|20}} 26 || Feb Mar Nov || Sep Dec || Jan Oct || {{red|Feb}} Aug || {{figure space}}{{figure space}} 09 15 {{red|20}} 26
|-
| {{red|04}} 10 {{figure space}}{{figure space}} 21 27 || {{red|Feb}} Aug || Jun || {{red|Jan}} Apr Jul || May || {{red|04}} 10 {{figure space}}{{figure space}} 21 27
|-
| 05 11 {{red|16}} 22 {{figure space}}{{figure space}} || May || Feb Mar Nov || Sep Dec || Jan Oct || 05 11 {{red|16}} 22 {{figure space}}{{figure space}}
|}