Common year starting on Friday

A common year starting on Friday is any non-leap year (i.e. a year with 365 days) that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2021 and the next one will be 2027 in the Gregorian calendar,[1] or, likewise, 2011 and 2022 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 100 when divided by 400. The most recent such year was 1700 and the next one will be 2100.

Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th: the only one in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.

In this common year, February is rectangular where weeks start on Monday, Martin Luther King Jr. Day is on January 18, Valentine’s Day is on a Sunday, Presidents Day is on its earliest possible date, February 15, St. Patrick’s Day is on a Wednesday, Memorial Day is on its latest possible date, May 31, Juneteenth is on a Saturday, U.S. Independence Day and Halloween are on Sunday, Labor Day is on September 6, Columbus Day is on October 11, Election Day in the United States is on its earliest possible date, November 2, Thanksgiving is on November 25, and Christmas is on a Saturday.

CalendarsEdit

Calendar for any common year starting on Friday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  
February
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28  
 
March
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 
April
Su Mo Tu We Th Fr Sa
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
 
May
Su Mo Tu We Th Fr Sa
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31  
June
Su Mo Tu We Th Fr Sa
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30  
 
July
Su Mo Tu We Th Fr Sa
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
 
August
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31  
 
September
Su Mo Tu We Th Fr Sa
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30  
 
October
Su Mo Tu We Th Fr Sa
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  
November
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30  
 
December
Su Mo Tu We Th Fr Sa
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31  
 
ISO 8601-conformant calendar with week numbers for
any common year starting on Friday (dominical letter C)
January
Wk Mo Tu We Th Fr Sa Su
53 01 02 03
01 04 05 06 07 08 09 10
02 11 12 13 14 15 16 17
03 18 19 20 21 22 23 24
04 25 26 27 28 29 30 31
   
February
Wk Mo Tu We Th Fr Sa Su
05 01 02 03 04 05 06 07
06 08 09 10 11 12 13 14
07 15 16 17 18 19 20 21
08 22 23 24 25 26 27 28
 
   
March
Wk Mo Tu We Th Fr Sa Su
09 01 02 03 04 05 06 07
10 08 09 10 11 12 13 14
11 15 16 17 18 19 20 21
12 22 23 24 25 26 27 28
13 29 30 31  
   
April
Wk Mo Tu We Th Fr Sa Su
13 01 02 03 04
14 05 06 07 08 09 10 11
15 12 13 14 15 16 17 18
16 19 20 21 22 23 24 25
17 26 27 28 29 30  
   
May
Wk Mo Tu We Th Fr Sa Su
17 01 02
18 03 04 05 06 07 08 09
19 10 11 12 13 14 15 16
20 17 18 19 20 21 22 23
21 24 25 26 27 28 29 30
22 31  
June
Wk Mo Tu We Th Fr Sa Su
22 01 02 03 04 05 06
23 07 08 09 10 11 12 13
24 14 15 16 17 18 19 20
25 21 22 23 24 25 26 27
26 28 29 30  
   
July
Wk Mo Tu We Th Fr Sa Su
26 01 02 03 04
27 05 06 07 08 09 10 11
28 12 13 14 15 16 17 18
29 19 20 21 22 23 24 25
30 26 27 28 29 30 31  
   
August
Wk Mo Tu We Th Fr Sa Su
30 01
31 02 03 04 05 06 07 08
32 09 10 11 12 13 14 15
33 16 17 18 19 20 21 22
34 23 24 25 26 27 28 29
35 30 31  
September
Wk Mo Tu We Th Fr Sa Su
35 01 02 03 04 05
36 06 07 08 09 10 11 12
37 13 14 15 16 17 18 19
38 20 21 22 23 24 25 26
39 27 28 29 30  
   
October
Wk Mo Tu We Th Fr Sa Su
39 01 02 03
40 04 05 06 07 08 09 10
41 11 12 13 14 15 16 17
42 18 19 20 21 22 23 24
43 25 26 27 28 29 30 31
   
November
Wk Mo Tu We Th Fr Sa Su
44 01 02 03 04 05 06 07
45 08 09 10 11 12 13 14
46 15 16 17 18 19 20 21
47 22 23 24 25 26 27 28
48 29 30  
   
December
Wk Mo Tu We Th Fr Sa Su
48 01 02 03 04 05
49 06 07 08 09 10 11 12
50 13 14 15 16 17 18 19
51 20 21 22 23 24 25 26
52 27 28 29 30 31  
   

This is the only year type where the nth "Doomsday" (this year Sunday) is not in ISO week n; it is in ISO week n-1.

Applicable yearsEdit

Gregorian calendarEdit

In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Saturday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Friday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Friday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1593 1599
17th century 1610 1621 1627 1638 1649 1655 1666 1677 1683 1694 1700
18th century 1706 1717 1723 1734 1745 1751 1762 1773 1779 1790
19th century 1802 1813 1819 1830 1841 1847 1858 1869 1875 1886 1897
20th century 1909 1915 1926 1937 1943 1954 1965 1971 1982 1993 1999
21st century 2010 2021 2027 2038 2049 2055 2066 2077 2083 2094 2100
22nd century 2106 2117 2123 2134 2145 2151 2162 2173 2179 2190
23rd century 2202 2213 2219 2230 2241 2247 2258 2269 2275 2286 2297
24th century 2309 2315 2326 2337 2343 2354 2365 2371 2382 2393 2399

400 year cycle:

  • century 1: 010, 021, 027, 038, 049, 055, 066, 077, 083, 094, 100
  • century 2: 106, 117, 123, 134, 145, 151, 162, 173, 179, 190
  • century 3: 202, 213, 219, 230, 241, 247, 258, 269, 275, 286, 297
  • century 4: 309, 315, 326, 337, 343, 354, 365, 371, 382, 393, 399

Julian calendarEdit

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). This sequence occurs exactly once within a cycle, and every common letter thrice.

As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1). Years 4, 15 and 26 of the cycle are common years beginning on Friday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Friday.

Julian common years starting on Friday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1406 1417 1423 1434 1445 1451 1462 1473 1479 1490
16th century 1501 1507 1518 1529 1535 1546 1557 1563 1574 1585 1591
17th century 1602 1613 1619 1630 1641 1647 1658 1669 1675 1686 1697
18th century 1703 1714 1725 1731 1742 1753 1759 1770 1781 1787 1798
19th century 1809 1815 1826 1837 1843 1854 1865 1871 1882 1893 1899
20th century 1910 1921 1927 1938 1949 1955 1966 1977 1983 1994
21st century 2005 2011 2022 2033 2039 2050 2061 2067 2078 2089 2095

ReferencesEdit

  1. ^ a b Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.