Common year starting on Saturday

A common year starting on Saturday is any non-leap year (i.e. a year with 365 days) that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2011 and the next one will be 2022 in the Gregorian calendar[1] or, likewise, 2017 and 2023 in the obsolete Julian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in May. Leap years starting on Friday share this characteristic.

Calendars

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

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  
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  
 
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  
 
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
 
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  
 
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  
 
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  
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  
 
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
 
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  
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  
 
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 Saturday (dominical letter B)

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  
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
 
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
 
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  
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  
 
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  
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  
 
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  
 
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  
 
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  
 
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  
 
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  
 

If the preceding year is a common year starting on Friday, then the year begins in ISO week 52; if the preceding year is a leap year starting on Thursday, then the year begins in ISO week 53.

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-three common years per cycle or exactly 10.75% start on a Saturday. The 28-year sub-cycle will break at a century year which is not divisible by 400 (e.g. it broke at the year 1900 but not at the year 2000).

Gregorian common years starting on Saturday[1]
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1583 1594
17th century 1605 1611 1622 1633 1639 1650 1661 1667 1678 1689 1695
18th century 1701 1707 1718 1729 1735 1746 1757 1763 1774 1785 1791
19th century 1803 1814 1825 1831 1842 1853 1859 1870 1881 1887 1898
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

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 in the Church of England, as 29 February has no letter). Each of the seven two-letter sequences occurs 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 10, 16 and 27 of the cycle are common years beginning on Saturday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Saturday.

Julian common years starting on Saturday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1401 1407 1418 1429 1435 1446 1457 1463 1474 1485 1491
16th century 1502 1513 1519 1530 1541 1547 1558 1569 1575 1586 1597
17th century 1603 1614 1625 1631 1642 1653 1659 1670 1681 1687 1698
18th century 1709 1715 1726 1737 1743 1754 1765 1771 1782 1793 1799
19th century 1810 1821 1827 1838 1849 1855 1866 1877 1883 1894
20th century 1905 1911 1922 1933 1939 1950 1961 1967 1978 1989 1995
21st century 2006 2017 2023 2034 2045 2051 2062 2073 2079 2090

References

  1. ^ a b c Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
1099

Year 1099 (MXCIX) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1138

Year 1138 (MCXXXVIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1155

Year 1155 (MCLV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1166

1166 (MCLXVI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1194

Year 1194 (MCXCIV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1239

Year 1239 (MCCXXXIX) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1295

Year 1295 (MCCXCV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1323

Year 1323 (MCCCXXIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1334

Year 1334 (MCCCXXXIV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1351

Year 1351 (MCCCLI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1429

Year 1429 (MCDXXIX) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1463

Year 1463 (MCDLXIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1474

Year 1474 (MCDLXXIV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1491

Year 1491 (MCDXCI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1513

Year 1513 (MDXIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1541

Year 1541 (MDXLI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

1558

Year 1558 (MDLVIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

28 BC

Year 28 BC was either a common year starting on Saturday, Sunday or Monday or a leap year starting on Saturday or Sunday (link will display the full calendar) of the Julian calendar (the sources differ, see leap year error for further information) and a common year starting on Saturday of the Proleptic Julian calendar. At the time, it was known as the Year of the First Consulship of Octavian and Agrippa (or, less frequently, year 726 Ab urbe condita). The denomination 28 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

AD 1

AD 1 (I), 1 AD or 1 CE is the epoch year for the Anno Domini calendar era. It was the first year of the Common Era (CE), of the 1st millennium and of the 1st century. It was a common year starting on Saturday or Sunday, a common year starting on Saturday by the proleptic Julian calendar, and a common year starting on Monday by the proleptic Gregorian calendar. In its time, year 1 was known as the Year of the Consulship of Caesar and Paullus, named after Roman consuls Gaius Caesar and Lucius Aemilius Paullus, and less frequently, as year 754 AUC (ab urbe condita) within the Roman Empire. The denomination "AD 1" for this year has been in consistent use since the mid-medieval period when the anno Domini (AD) calendar era became the prevalent method in Europe for naming years. It was the beginning of the Christian/Common era. The preceding year is 1 BC; there is no year 0 in this numbering scheme. The Anno Domini dating system was devised in AD 525 by Dionysius Exiguus.

The Julian calendar, a 45 BC reform of the Roman calendar, was the calendar used by Rome in AD 1.

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