Leap year starting on Saturday

A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA. The most recent year of such kind was 2000, and the next one will be 2028 in the Gregorian calendar or, likewise 2012 and 2040 in the obsolete Julian calendar. In the Gregorian calendar, years divisible by 400 are always leap years starting on Saturday. The most recent such occurrence was 2000 and the next one will be 2400, see below for more.[1]

Any leap year that starts on Saturday has only one Friday the 13th: the only one in this leap year occurs in October. Common years starting on Sunday share this characteristic, but also have another in January. From August of the common year preceding that year until October in this type of year is also the longest period (14 months) that occurs without a Friday the 13th. Common years starting on Tuesday share this characteristic, from July of the year that precedes it to September in that type of year.

Calendars

Calendar for any leap year starting on Saturday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
1
2345678
9101112131415
16171819202122
23242526272829
3031  
February
Su Mo Tu We Th Fr Sa
12345
6789101112
13141516171819
20212223242526
272829  
 
March
Su Mo Tu We Th Fr Sa
1234
567891011
12131415161718
19202122232425
262728293031  
 
April
Su Mo Tu We Th Fr Sa
1
2345678
9101112131415
16171819202122
23242526272829
30  
May
Su Mo Tu We Th Fr Sa
123456
78910111213
14151617181920
21222324252627
28293031  
 
June
Su Mo Tu We Th Fr Sa
123
45678910
11121314151617
18192021222324
252627282930
 
July
Su Mo Tu We Th Fr Sa
1
2345678
9101112131415
16171819202122
23242526272829
3031  
August
Su Mo Tu We Th Fr Sa
12345
6789101112
13141516171819
20212223242526
2728293031  
 
September
Su Mo Tu We Th Fr Sa
12
3456789
10111213141516
17181920212223
24252627282930
 
October
Su Mo Tu We Th Fr Sa
1234567
891011121314
15161718192021
22232425262728
293031  
 
November
Su Mo Tu We Th Fr Sa
1234
567891011
12131415161718
19202122232425
2627282930  
 
December
Su Mo Tu We Th Fr Sa
12
3456789
10111213141516
17181920212223
24252627282930
31  
ISO 8601-conformant calendar with week numbers for
any leap year starting on Saturday (dominical letter BA)
January
Wk Mo Tu We Th Fr Sa Su
52 0102
01 03040506070809
02 10111213141516
03 17181920212223
04 24252627282930
05 31  
February
Wk Mo Tu We Th Fr Sa Su
05 010203040506
06 07080910111213
07 14151617181920
08 21222324252627
09 2829  
   
March
Wk Mo Tu We Th Fr Sa Su
09 0102030405
10 06070809101112
11 13141516171819
12 20212223242526
13 2728293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 0102
14 03040506070809
15 10111213141516
16 17181920212223
17 24252627282930
   
May
Wk Mo Tu We Th Fr Sa Su
18 01020304050607
19 08091011121314
20 15161718192021
21 22232425262728
22 293031  
   
June
Wk Mo Tu We Th Fr Sa Su
22 01020304
23 05060708091011
24 12131415161718
25 19202122232425
26 2627282930  
   
July
Wk Mo Tu We Th Fr Sa Su
26 0102
27 03040506070809
28 10111213141516
29 17181920212223
30 24252627282930
31 31  
August
Wk Mo Tu We Th Fr Sa Su
31 010203040506
32 07080910111213
33 14151617181920
34 21222324252627
35 28293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 010203
36 04050607080910
37 11121314151617
38 18192021222324
39 252627282930
   
October
Wk Mo Tu We Th Fr Sa Su
39 01
40 02030405060708
41 09101112131415
42 16171819202122
43 23242526272829
44 3031  
November
Wk Mo Tu We Th Fr Sa Su
44 0102030405
45 06070809101112
46 13141516171819
47 20212223242526
48 27282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 010203
49 04050607080910
50 11121314151617
51 18192021222324
52 25262728293031
   

Applicable years

Gregorian Calendar

Leap years that begin on Saturday, along with those starting on Monday and Thursday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).

Gregorian leap years starting on Saturday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic)1600
17th century 162816561684
18th century 172417521780
19th century 182018481876
20th century 1916194419722000
21st century 202820562084
22nd century 212421522180
23rd century 222022482276
24th century 2316234423722400
25th century 242824562484
400-year cycle
0–99 0285684
100–199 124152180
200–299 220248276
300–399 316344372

Julian Calendar

Like all leap year types, the one starting with 1 January on a Saturday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. 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).

Julian leap years starting on Saturday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 142414521480
16th century 1508153615641592
17th century 162016481676
18th century 1704173217601788
19th century 1816184418721900
20th century 192819561984
21st century 2012204020682096
22nd century 212421522180

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

Denmark

Germany

United States

References

Wikimedia Commons logo
Wikimedia Commons has media related to Leap years starting on Saturday and ending on Sunday.
  1. 1 2 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
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