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Leap year starting on Monday

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A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF. The current year, 2024, is a leap year starting on Monday in the Gregorian calendar. The last such year was 1996 and the next such year will be 2052 in the Gregorian calendar or, likewise, 2008 and 2036 in the obsolete Julian calendar. 29 February falls on Thursday.

Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths: those two in this leap year occur in September and December. Common years starting on Tuesday share this characteristic.

Additionally, this type of year has three months (January, April, and July) beginning exactly on the first day of the week, in areas which Monday is considered the first day of the week, Common years starting on Friday share this characteristic on the months of February, March, and November.

Calendars

Calendar for any leap year starting on Monday,
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 29
 
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 leap year starting on Monday (dominical letter GF)
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  
   

Applicable years

Gregorian Calendar

Leap years that begin on Monday, along with those starting on Saturday 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 Monday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1596
17th century 1624 1652 1680
18th century 1720 1748 1776
19th century 1816 1844 1872
20th century 1912 1940 1968 1996
21st century 2024 2052 2080
22nd century 2120 2148 2176
23rd century 2216 2244 2272
24th century 2312 2340 2368 2396
25th century 2424 2452 2480
26th century 2520 2548 2576
27th century 2616 2644 2672
400-year cycle
0–99 24 52 80
100–199 120 148 176
200–299 216 244 272
300–399 312 340 368 396

Julian Calendar

Like all leap year types, the one starting with 1 January on a Monday 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 Monday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
14th century 1308 1336 1364 1392
15th century 1420 1448 1476
16th century 1504 1532 1560 1588
17th century 1616 1644 1672 1700
18th century 1728 1756 1784
19th century 1812 1840 1868 1896
20th century 1924 1952 1980
21st century 2008 2036 2064 2092
22nd century 2120 2148 2176

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

References

  1. ^ Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
Gregorian year types per leap cycle by Dominical letter (DL) and Doomsday (DD)
Year starts Common years Leap years
1 Jan Count Ratio 31 Dec DL DD Count Ratio 31 Dec DL DD Count Ratio
Sun 58 14.50 % Sun A Tue 43 10.75 % Mon AG Wed 15 03.75 %
Sat 56 14.00 % Sat B Mon 43 10.75 % Sun BA Tue 13 03.25 %
Fri 58 14.50 % Fri C Sun 43 10.75 % Sat CB Mon 15 03.75 %
Thu 57 14.25 % Thu D Sat 44 11.00 % Fri DC Sun 13 03.25 %
Wed 57 14.25 % Wed E Fri 43 10.75 % Thu ED Sat 14 03.50 %
Tue 58 14.50 % Tue F Thu 44 11.00 % Wed FE Fri 14 03.50 %
Mon 56 14.00 % Mon G Wed 43 10.75 % Tue GF Thu 13 03.25 %
400 100.0 % 303 75.75 % 97 24.25 %
Source: Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
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