Leap year starting on Monday

Last updated

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, such as the years 1912, 1940, 1968, 1996, 2024, 2052, 2080, and 2120 in the Gregorian calendar [1] or, likewise, 2008, 2036, and 2064 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in September and December. Common years starting on Tuesday share this characteristic.

Contents

Calendars

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

010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
010203
04050607080910
11121314151617
18192021222324
2526272829
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
010203040506
07080910111213
14151617181920
21222324252627
282930 
 
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 

ISO 8601-conformant calendar with week numbers for
any leap year starting on Monday (dominical letter GF)

01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
01020304050607
08091011121314
15161718192021
22232425262728
2930 
 
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
01020304
05060708091011
12131415161718
19202122232425
26272829 
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031 
 
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
010203
04050607080910
11121314151617
18192021222324
252627282930
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
01
02030405060708
09101112131415
16171819202122
23242526272829
30 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 

Applicable years

Gregorian Calendar

Leap years that begin on Monday, along with those that start on Saturday or Thursday, occur least frequently: 13 out of 97 (≈ 13.4%) total leap years of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).

Gregorian leap years starting on Monday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
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

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
Decade1st2nd3rd4th5th6th7th8th9th10th
14th century 1308 1336 1364 1392
15th century 1420 1448 1476
16th century 1504 1532 1560 1588
17th century 1616 1644 1672 1700
18th century172817561784
19th century1812184018681896
20th century192419521980
21st century2008203620642092
22nd century212021482176

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.