Common year starting on Thursday

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A common year starting on Thursday is any non-leap year (i.e. a year with 365 days) that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar [1] or, likewise, 2010 and 2021 in the obsolete Julian calendar, see below for more. This common year contains the most Friday the 13ths; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic. From February until March in this type of year is also the shortest period (one month) that occurs within a Friday the 13th.

Contents

Calendars

Calendar for any common year starting on Thursday,
presented as common in many English-speaking areas

010203
04050607080910
11121314151617
18192021222324
25262728293031
 
01020304050607
08091011121314
15161718192021
22232425262728
 
 
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
01020304
05060708091011
12131415161718
19202122232425
2627282930 
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
010203040506
07080910111213
14151617181920
21222324252627
282930 
 
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
0102030405
06070809101112
13141516171819
20212223242526
27282930 
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 

ISO 8601-conformant calendar with week numbers for
any common year starting on Thursday (dominical letter D)

01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
0102030405
06070809101112
13141516171819
20212223242526
27282930 
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
01
02030405060708
09101112131415
16171819202122
232425262728
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
010203040506
07080910111213
14151617181920
21222324252627
282930 
 
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Thursday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Thursday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1587 1598
17th century 1609 1615 1626 1637 1643 1654 1665 1671 1682 1693 1699
18th century 1705 1711 1722 1733 1739 1750 1761 1767 1778 1789 1795
19th century 1801 1807 1818 1829 1835 1846 1857 1863 1874 1885 1891
20th century 1903 1914 1925 1931 1942 1953 1959 1970 1981 1987 1998
21st century 2009 2015 2026 2037 2043 2054 2065 2071 2082 2093 2099

Julian Calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters (one for January and February and the other for March to December, as 29 February has no letter). 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 3, 14 and 20 of the cycle are common years beginning on Thursday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Thursday.

Julian common years starting on Thursday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1405 1411 1422 1433 1439 1450 1461 1467 1478 1489 1495
16th century 1506 1517 1523 1534 1545 1551 1562 1573 1579 1590
17th century16011607161816291635164616571663167416851691
18th century17021713171917301741174717581769177517861797
19th century18031814182518311842185318591870188118871898
20th century19091915192619371943195419651971198219931999
21st century2010202120272038204920552066207720832094

References

  1. 1 2 3 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.