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Common year starting on Saturday

From Wikipedia, the free encyclopedia

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 2022 and the next one will be 2033 in the Gregorian calendar[1] or, likewise, 2023 and 2034 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 one in this common year occurs in May.

From July of the year that precedes this year until September in this type of year is the longest period (14 months) that occurs without a Tuesday the 13th.

Calendars

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

Applicable years

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Gregorian Calendar

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In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Friday, 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
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
22nd century 2101 2107 2118 2129 2135 2146 2157 2163 2174 2185 2191
23rd century 2203 2214 2225 2231 2242 2253 2259 - 2270 2281 2287 2298
24th century 2310 2321 2327 2338 2349 2355 2366 2377 2383 2394
25th century 2405 2411 2422 2433 2439 2450 2461 2467 2478 2489 2495
400-year cycle
0–99 5 11 22 33 39 50 61 67 78 89 95
100–199 101 107 118 129 135 146 157 163 174 185 191
200–299 203 214 225 231 242 253 259 270 281 287 298
300–399 310 321 327 338 349 355 366 377 383 394

Julian Calendar

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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

Holidays

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International

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Roman Catholic Solemnities

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Australia and New Zealand

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British Isles

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Canada

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United States

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References

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