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Hebrew Calendar Science and Myths
34 Day Variance Hebrew Year Periods

by Remy Landau
=================================

Properties of Hebrew Year Periods shows that while a given Hebrew year period has only
one length in years, it can have up to 2 lengths in terms of months,
and up to 10 lengths in terms of days.

The following tables show the fully extrapolated molad periods, the month counts, the day counts, the modulo reduction by 7d of the number of days in each of the entries, the statistical distributions of the various lengths over the Hebrew calendar cycle of 689,472 years, and the maximum variance in days for the given period of Hebrew years.

The maximum variance is the difference between the longest and the shortest possible lengths in days for a given period of Hebrew years.

As shown by 23. The 34 Day Maximum Variance, The maximum possible variance for any period of Hebrew years is 34 days.

Properties 24, 25, and 26 prove that the 34 day maximum variance occurs whenever a period of Hebrew years meets the following conditions

2h 491p < m' < 8h 876p and M' MOD 7 = 6 15h 204p < m" < 21h 588p and M" MOD 7 = 0
Since the second condition follows from the first, only the first set of conditions need be statisfied.

For more information please refer to

24. M' MOD 7d When L" - L' = 34d
25. M" MOD 7d When L" - L' = 34d
26. Limits to m' and m" When L" - L' = 34d

Out of the first 2,000 spans, 71 were found to satisfy all of the above conditions.

The structure of these tables is explained in Properties of Hebrew Year Periods - Introduction.

10 YEAR SPANS
    123 months =     3,632d  6h  339p
    124 months =     3,661d 19h   52p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
     3,630d
4
   3,236
-2
         0d
0
       0
-1
     3,631d
5
  76,946
-1
         0d
0
       0
0
     3,632d
6
  22,866
0
     3,661d
0
 252,669
1
     3,633d
0
 114,680
1
     3,662d
1
  47,195
2
         0d
0
       0
2
     3,663d
2
 162,407
3
         0d
0
       0
3
     3,664d
3
   9,473
The maximum variance is 34 days

68 YEAR SPANS
    841 months =    24,835d  5h  553p
    842 months =    24,864d 18h  266p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    24,833d
4
   5,370
-2
         0d
0
       0
-1
    24,834d
5
 212,176
-1
         0d
0
       0
0
    24,835d
6
  67,041
0
    24,864d
0
  18,751
1
    24,836d
0
 368,597
1
    24,865d
1
   3,811
2
         0d
0
       0
2
    24,866d
2
  13,066
3
         0d
0
       0
3
    24,867d
3
     660
The maximum variance is 34 days

81 YEAR SPANS
  1,001 months =    29,560d  2h 1073p
  1,002 months =    29,589d 15h  786p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    29,558d
4
   3,770
-2
         0d
0
       0
-1
    29,559d
5
  42,776
-1
         0d
0
       0
0
    29,560d
6
  11,433
0
    29,589d
0
 356,818
1
    29,561d
0
  50,885
1
    29,590d
1
  55,015
2
         0d
0
       0
2
    29,591d
2
 167,844
3
         0d
0
       0
3
    29,592d
3
     931
The maximum variance is 34 days

88 YEAR SPANS
  1,088 months =    32,129d  6h  944p
  1,089 months =    32,158d 19h  657p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    32,127d
4
   4,602
-2
         0d
0
       0
-1
    32,128d
5
 130,793
-1
         0d
0
       0
0
    32,129d
6
  39,801
0
    32,158d
0
 145,375
1
    32,130d
0
 223,972
1
    32,159d
1
  29,958
2
         0d
0
       0
2
    32,160d
2
 107,334
3
         0d
0
       0
3
    32,161d
3
   7,637
The maximum variance is 34 days

108 YEAR SPANS
  1,335 months =    39,423d  8h  255p
  1,336 months =    39,452d 20h 1048p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    39,421d
4
     497
-2
         0d
0
       0
-1
    39,422d
5
  47,976
-1
         0d
0
       0
0
    39,423d
6
  15,244
0
    39,452d
0
 276,205
1
    39,424d
0
  81,435
1
    39,453d
1
  56,670
2
         0d
0
       0
2
    39,454d
2
 198,050
3
         0d
0
       0
3
    39,455d
3
  13,395
The maximum variance is 34 days

159 YEAR SPANS
  1,966 months =    58,057d  3h  598p
  1,967 months =    58,086d 16h  311p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    58,055d
4
   9,085
-2
         0d
0
       0
-1
    58,056d
5
 110,230
-1
         0d
0
       0
0
    58,057d
6
  29,958
0
    58,086d
0
 229,945
1
    58,058d
0
 141,031
1
    58,087d
1
  39,801
2
         0d
0
       0
2
    58,088d
2
 126,811
3
         0d
0
       0
3
    58,089d
3
   2,611
The maximum variance is 34 days

166 YEAR SPANS
  2,053 months =    60,626d  7h  469p
  2,054 months =    60,655d 20h  182p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    60,624d
4
   2,379
-2
         0d
0
       0
-1
    60,625d
5
 175,084
-1
         0d
0
       0
0
    60,626d
6
  56,463
0
    60,655d
0
  52,514
1
    60,627d
0
 346,682
1
    60,656d
1
  11,433
2
         0d
0
       0
2
    60,657d
2
  41,690
3
         0d
0
       0
3
    60,658d
3
   3,227
The maximum variance is 34 days

179 YEAR SPANS
  2,213 months =    65,351d  4h  989p
  2,214 months =    65,380d 17h  702p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    65,349d
4
     841
-2
         0d
0
       0
-1
    65,350d
5
  13,428
-1
         0d
0
       0
0
    65,351d
6
   3,811
0
    65,380d
0
 379,457
1
    65,352d
0
  18,208
1
    65,381d
1
  65,955
2
         0d
0
       0
2
    65,382d
2
 204,574
3
         0d
0
       0
3
    65,383d
3
   3,198
The maximum variance is 34 days

186 YEAR SPANS
  2,300 months =    67,920d  8h  860p
  2,301 months =    67,949d 21h  573p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    67,918d
4
      29
-2
         0d
0
       0
-1
    67,919d
5
 101,961
-1
         0d
0
       0
0
    67,920d
6
  33,239
0
    67,949d
0
 173,520
1
    67,921d
0
 191,363
1
    67,950d
1
  36,520
2
         0d
0
       0
2
    67,951d
2
 139,142
3
         0d
0
       0
3
    67,952d
3
  13,698
The maximum variance is 34 days

237 YEAR SPANS
  2,931 months =    86,554d  4h  123p
  2,932 months =    86,583d 16h  916p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    86,552d
4
  11,645
-2
         0d
0
       0
-1
    86,553d
5
 167,294
-1
         0d
0
       0
0
    86,554d
6
  47,376
0
    86,583d
0
 117,938
1
    86,555d
0
 245,429
1
    86,584d
1
  22,866
2
         0d
0
       0
2
    86,585d
2
  74,774
3
         0d
0
       0
3
    86,586d
3
   2,150
The maximum variance is 34 days

257 YEAR SPANS
  3,178 months =    93,848d  5h  514p
  3,179 months =    93,877d 18h  227p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
    93,846d
4
   4,322
-2
         0d
0
       0
-1
    93,847d
5
  79,118
-1
         0d
0
       0
0
    93,848d
6
  22,866
0
    93,877d
0
 259,909
1
    93,849d
0
 111,422
1
    93,878d
1
  47,014
2
         0d
0
       0
2
    93,879d
2
 157,520
3
         0d
0
       0
3
    93,880d
3
   7,301
The maximum variance is 34 days

315 YEAR SPANS
  3,896 months =   115,051d  4h  728p
  3,897 months =   115,080d 17h  441p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   115,049d
4
   7,542
-2
         0d
0
       0
-1
   115,050d
5
 219,778
-1
         0d
0
       0
0
   115,051d
6
  68,127
0
   115,080d
0
  19,294
1
   115,052d
0
 357,737
1
   115,081d
1
   3,811
2
         0d
0
       0
2
   115,082d
2
  12,704
3
         0d
0
       0
3
   115,083d
3
     479
The maximum variance is 34 days

335 YEAR SPANS
  4,143 months =   122,345d  6h   39p
  4,144 months =   122,374d 18h  832p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   122,343d
4
   6,593
-2
         0d
0
       0
-1
   122,344d
5
 134,775
-1
         0d
0
       0
0
   122,345d
6
  39,801
0
   122,374d
0
 149,719
1
   122,346d
0
 217,999
1
   122,375d
1
  29,958
2
         0d
0
       0
2
   122,376d
2
 104,438
3
         0d
0
       0
3
   122,377d
3
   6,189
The maximum variance is 34 days

355 YEAR SPANS
  4,390 months =   129,639d  7h  430p
  4,391 months =   129,668d 20h  143p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   129,637d
4
   1,221
-2
         0d
0
       0
-1
   129,638d
5
  49,424
-1
         0d
0
       0
0
   129,639d
6
  15,244
0
   129,668d
0
 284,893
1
   129,640d
0
  79,263
1
   129,669d
1
  56,127
2
         0d
0
       0
2
   129,670d
2
 192,077
3
         0d
0
       0
3
   129,671d
3
  11,223
The maximum variance is 34 days

406 YEAR SPANS
  5,021 months =   148,273d  2h  773p
  5,022 months =   148,302d 15h  486p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   148,271d
4
  10,533
-2
         0d
0
       0
-1
   148,272d
5
 113,126
-1
         0d
0
       0
0
   148,273d
6
  29,958
0
   148,302d
0
 235,918
1
   148,274d
0
 136,687
1
   148,303d
1
  39,801
2
         0d
0
       0
2
   148,304d
2
 122,829
3
         0d
0
       0
3
   148,305d
3
     620
The maximum variance is 34 days

413 YEAR SPANS
  5,108 months =   150,842d  6h  644p
  5,109 months =   150,871d 19h  357p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   150,840d
4
   3,827
-2
         0d
0
       0
-1
   150,841d
5
 182,324
-1
         0d
0
       0
0
   150,842d
6
  57,911
0
   150,871d
0
  54,143
1
   150,843d
0
 336,546
1
   150,872d
1
  11,433
2
         0d
0
       0
2
   150,873d
2
  40,604
3
         0d
0
       0
3
   150,874d
3
   2,684
The maximum variance is 34 days

426 YEAR SPANS
  5,268 months =   155,567d  4h   84p
  5,269 months =   155,596d 16h  877p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   155,565d
4
   1,022
-2
         0d
0
       0
-1
   155,566d
5
  13,790
-1
         0d
0
       0
0
   155,567d
6
   3,811
0
   155,596d
0
 391,395
1
   155,568d
0
  17,665
1
   155,597d
1
  63,791
2
         0d
0
       0
2
   155,598d
2
 195,894
3
         0d
0
       0
3
   155,599d
3
   2,104
The maximum variance is 34 days

433 YEAR SPANS
  5,355 months =   158,136d  7h 1035p
  5,356 months =   158,165d 20h  748p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   158,134d
4
   1,658
-2
         0d
0
       0
-1
   158,135d
5
 105,219
-1
         0d
0
       0
0
   158,136d
6
  33,239
0
   158,165d
0
 178,950
1
   158,137d
0
 186,476
1
   158,166d
1
  36,520
2
         0d
0
       0
2
   158,167d
2
 135,522
3
         0d
0
       0
3
   158,168d
3
  11,888
The maximum variance is 34 days

484 YEAR SPANS
  5,986 months =   176,770d  3h  298p
  5,987 months =   176,799d 16h   11p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   176,768d
4
  13,817
-2
         0d
0
       0
-1
   176,769d
5
 172,181
-1
         0d
0
       0
0
   176,770d
6
  47,557
0
   176,799d
0
 121,196
1
   176,771d
0
 238,189
1
   176,800d
1
  22,866
2
         0d
0
       0
2
   176,801d
2
  72,602
3
         0d
0
       0
3
   176,802d
3
   1,064
The maximum variance is 34 days

504 YEAR SPANS
  6,233 months =   184,064d  4h  689p
  6,234 months =   184,093d 17h  402p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   184,062d
4
   5,408
-2
         0d
0
       0
-1
   184,063d
5
  81,290
-1
         0d
0
       0
0
   184,064d
6
  22,866
0
   184,093d
0
 267,208
1
   184,065d
0
 108,164
1
   184,094d
1
  46,774
2
         0d
0
       0
2
   184,095d
2
 152,574
3
         0d
0
       0
3
   184,096d
3
   5,188
The maximum variance is 34 days

511 YEAR SPANS
  6,320 months =   186,633d  8h  560p
  6,321 months =   186,662d 21h  273p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   186,631d
4
     632
-2
         0d
0
       0
-1
   186,632d
5
 149,332
-1
         0d
0
       0
0
   186,633d
6
  48,835
0
   186,662d
0
  84,010
1
   186,634d
0
 309,233
1
   186,663d
1
  19,055
2
         0d
0
       0
2
   186,664d
2
  71,826
3
         0d
0
       0
3
   186,665d
3
   6,549
The maximum variance is 34 days

562 YEAR SPANS
  6,951 months =   205,267d  3h  903p
  6,952 months =   205,296d 16h  616p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   205,265d
4
   9,714
-2
         0d
0
       0
-1
   205,266d
5
 227,380
-1
         0d
0
       0
0
   205,267d
6
  69,213
0
   205,296d
0
  19,837
1
   205,268d
0
 346,877
1
   205,297d
1
   3,811
2
         0d
0
       0
2
   205,298d
2
  12,342
3
         0d
0
       0
3
   205,299d
3
     298
The maximum variance is 34 days

582 YEAR SPANS
  7,198 months =   212,561d  5h  214p
  7,199 months =   212,590d 17h 1007p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   212,559d
4
   8,584
-2
         0d
0
       0
-1
   212,560d
5
 138,757
-1
         0d
0
       0
0
   212,561d
6
  39,801
0
   212,590d
0
 154,063
1
   212,562d
0
 212,026
1
   212,591d
1
  29,958
2
         0d
0
       0
2
   212,592d
2
 101,542
3
         0d
0
       0
3
   212,593d
3
   4,741
The maximum variance is 34 days

602 YEAR SPANS
  7,445 months =   219,855d  6h  605p
  7,446 months =   219,884d 19h  318p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   219,853d
4
   1,945
-2
         0d
0
       0
-1
   219,854d
5
  50,872
-1
         0d
0
       0
0
   219,855d
6
  15,244
0
   219,884d
0
 293,581
1
   219,856d
0
  77,091
1
   219,885d
1
  55,584
2
         0d
0
       0
2
   219,886d
2
 186,104
3
         0d
0
       0
3
   219,887d
3
   9,051
The maximum variance is 34 days

660 YEAR SPANS
  8,163 months =   241,058d  5h  819p
  8,164 months =   241,087d 18h  532p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   241,056d
4
   5,792
-2
         0d
0
       0
-1
   241,057d
5
 189,047
-1
         0d
0
       0
0
   241,058d
6
  58,842
0
   241,087d
0
  55,772
1
   241,059d
0
 326,927
1
   241,088d
1
  11,433
2
         0d
0
       0
2
   241,089d
2
  39,518
3
         0d
0
       0
3
   241,090d
3
   2,141
The maximum variance is 34 days

673 YEAR SPANS
  8,323 months =   245,783d  3h  259p
  8,324 months =   245,812d 15h 1052p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   245,781d
4
   1,203
-2
         0d
0
       0
-1
   245,782d
5
  14,152
-1
         0d
0
       0
0
   245,783d
6
   3,811
0
   245,812d
0
 403,341
1
   245,784d
0
  17,122
1
   245,813d
1
  61,619
2
         0d
0
       0
2
   245,814d
2
 187,206
3
         0d
0
       0
3
   245,815d
3
   1,018
The maximum variance is 34 days

680 YEAR SPANS
  8,410 months =   248,352d  7h  130p
  8,411 months =   248,381d 19h  923p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   248,350d
4
   3,287
-2
         0d
0
       0
-1
   248,351d
5
 108,477
-1
         0d
0
       0
0
   248,352d
6
  33,239
0
   248,381d
0
 184,380
1
   248,353d
0
 181,589
1
   248,382d
1
  36,520
2
         0d
0
       0
2
   248,383d
2
 131,902
3
         0d
0
       0
3
   248,384d
3
  10,078
The maximum variance is 34 days

700 YEAR SPANS
  8,657 months =   255,646d  8h  521p
  8,658 months =   255,675d 21h  234p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   255,644d
4
     142
-2
         0d
0
       0
-1
   255,645d
5
  23,774
-1
         0d
0
       0
0
   255,646d
6
   7,622
0
   255,675d
0
 313,373
1
   255,647d
0
  41,038
1
   255,676d
1
  65,995
2
         0d
0
       0
2
   255,677d
2
 224,555
3
         0d
0
       0
3
   255,678d
3
  12,973
The maximum variance is 34 days

751 YEAR SPANS
  9,288 months =   274,280d  3h  864p
  9,289 months =   274,309d 16h  577p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   274,278d
4
   6,494
-2
         0d
0
       0
-1
   274,279d
5
  83,462
-1
         0d
0
       0
0
   274,280d
6
  22,866
0
   274,309d
0
 274,629
1
   274,281d
0
 104,906
1
   274,310d
1
  46,412
2
         0d
0
       0
2
   274,311d
2
 147,506
3
         0d
0
       0
3
   274,312d
3
   3,197
The maximum variance is 34 days

758 YEAR SPANS
  9,375 months =   276,849d  7h  735p
  9,376 months =   276,878d 20h  448p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   276,847d
4
   2,442
-2
         0d
0
       0
-1
   276,848d
5
 155,124
-1
         0d
0
       0
0
   276,849d
6
  49,559
0
   276,878d
0
  86,725
1
   276,850d
0
 300,907
1
   276,879d
1
  19,055
2
         0d
0
       0
2
   276,880d
2
  70,016
3
         0d
0
       0
3
   276,881d
3
   5,644
The maximum variance is 34 days

809 YEAR SPANS
 10,006 months =   295,483d  2h 1078p
 10,007 months =   295,512d 15h  791p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   295,481d
4
  11,886
-2
         0d
0
       0
-1
   295,482d
5
 234,982
-1
         0d
0
       0
0
   295,483d
6
  70,299
0
   295,512d
0
  20,380
1
   295,484d
0
 336,017
1
   295,513d
1
   3,811
2
         0d
0
       0
2
   295,514d
2
  11,980
3
         0d
0
       0
3
   295,515d
3
     117
The maximum variance is 34 days

829 YEAR SPANS
 10,253 months =   302,777d  4h  389p
 10,254 months =   302,806d 17h  102p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   302,775d
4
  10,575
-2
         0d
0
       0
-1
   302,776d
5
 142,739
-1
         0d
0
       0
0
   302,777d
6
  39,801
0
   302,806d
0
 158,407
1
   302,778d
0
 206,053
1
   302,807d
1
  29,958
2
         0d
0
       0
2
   302,808d
2
  98,646
3
         0d
0
       0
3
   302,809d
3
   3,293
The maximum variance is 34 days

849 YEAR SPANS
 10,500 months =   310,071d  5h  780p
 10,501 months =   310,100d 18h  493p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   310,069d
4
   2,669
-2
         0d
0
       0
-1
   310,070d
5
  52,320
-1
         0d
0
       0
0
   310,071d
6
  15,244
0
   310,100d
0
 302,269
1
   310,072d
0
  74,919
1
   310,101d
1
  55,041
2
         0d
0
       0
2
   310,102d
2
 180,131
3
         0d
0
       0
3
   310,103d
3
   6,879
The maximum variance is 34 days

907 YEAR SPANS
 11,218 months =   331,274d  4h  994p
 11,219 months =   331,303d 17h  707p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   331,272d
4
   7,964
-2
         0d
0
       0
-1
   331,273d
5
 195,563
-1
         0d
0
       0
0
   331,274d
6
  59,566
0
   331,303d
0
  57,401
1
   331,275d
0
 317,515
1
   331,304d
1
  11,433
2
         0d
0
       0
2
   331,305d
2
  38,432
3
         0d
0
       0
3
   331,306d
3
   1,598
The maximum variance is 34 days

927 YEAR SPANS
 11,465 months =   338,568d  6h  305p
 11,466 months =   338,597d 19h   18p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   338,566d
4
   4,916
-2
         0d
0
       0
-1
   338,567d
5
 111,735
-1
         0d
0
       0
0
   338,568d
6
  33,239
0
   338,597d
0
 189,810
1
   338,569d
0
 176,702
1
   338,598d
1
  36,520
2
         0d
0
       0
2
   338,599d
2
 128,282
3
         0d
0
       0
3
   338,600d
3
   8,268
The maximum variance is 34 days

947 YEAR SPANS
 11,712 months =   345,862d  7h  696p
 11,713 months =   345,891d 20h  409p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   345,860d
4
     504
-2
         0d
0
       0
-1
   345,861d
5
  24,498
-1
         0d
0
       0
0
   345,862d
6
   7,622
0
   345,891d
0
 323,509
1
   345,863d
0
  39,952
1
   345,892d
1
  65,090
2
         0d
0
       0
2
   345,893d
2
 217,496
3
         0d
0
       0
3
   345,894d
3
  10,801
The maximum variance is 34 days

998 YEAR SPANS
 12,343 months =   364,496d  2h 1039p
 12,344 months =   364,525d 15h  752p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   364,494d
4
   7,580
-2
         0d
0
       0
-1
   364,495d
5
  85,634
-1
         0d
0
       0
0
   364,496d
6
  22,866
0
   364,525d
0
 282,050
1
   364,497d
0
 101,648
1
   364,526d
1
  46,050
2
         0d
0
       0
2
   364,527d
2
 142,438
3
         0d
0
       0
3
   364,528d
3
   1,206
The maximum variance is 34 days

1,005 YEAR SPANS
 12,430 months =   367,065d  6h  910p
 12,431 months =   367,094d 19h  623p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   367,063d
4
   4,252
-2
         0d
0
       0
-1
   367,064d
5
 160,916
-1
         0d
0
       0
0
   367,065d
6
  50,283
0
   367,094d
0
  89,440
1
   367,066d
0
 292,581
1
   367,095d
1
  19,055
2
         0d
0
       0
2
   367,096d
2
  68,206
3
         0d
0
       0
3
   367,097d
3
   4,739
The maximum variance is 34 days

1,025 YEAR SPANS
 12,677 months =   374,359d  8h  221p
 12,678 months =   374,388d 20h 1014p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   374,357d
4
     917
-2
         0d
0
       0
-1
   374,358d
5
  84,052
-1
         0d
0
       0
0
   374,359d
6
  26,677
0
   374,388d
0
 216,233
1
   374,360d
0
 142,370
1
   374,389d
1
  43,081
2
         0d
0
       0
2
   374,390d
2
 161,238
3
         0d
0
       0
3
   374,391d
3
  14,904
The maximum variance is 34 days

1,076 YEAR SPANS
 13,308 months =   392,993d  3h  564p
 13,309 months =   393,022d 16h  277p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   392,991d
4
  12,566
-2
         0d
0
       0
-1
   392,992d
5
 146,721
-1
         0d
0
       0
0
   392,993d
6
  39,801
0
   393,022d
0
 162,751
1
   392,994d
0
 200,080
1
   393,023d
1
  29,958
2
         0d
0
       0
2
   393,024d
2
  95,750
3
         0d
0
       0
3
   393,025d
3
   1,845
The maximum variance is 34 days

1,096 YEAR SPANS
 13,555 months =   400,287d  4h  955p
 13,556 months =   400,316d 17h  668p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   400,285d
4
   3,393
-2
         0d
0
       0
-1
   400,286d
5
  53,768
-1
         0d
0
       0
0
   400,287d
6
  15,244
0
   400,316d
0
 310,973
1
   400,288d
0
  72,747
1
   400,317d
1
  54,482
2
         0d
0
       0
2
   400,318d
2
 174,142
3
         0d
0
       0
3
   400,319d
3
   4,723
The maximum variance is 34 days

1,103 YEAR SPANS
 13,642 months =   402,856d  8h  826p
 13,643 months =   402,885d 21h  539p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   402,854d
4
     120
-2
         0d
0
       0
-1
   402,855d
5
 131,670
-1
         0d
0
       0
0
   402,856d
6
  43,081
0
   402,885d
0
 116,498
1
   402,857d
0
 260,585
1
   402,886d
1
  26,677
2
         0d
0
       0
2
   402,887d
2
 101,300
3
         0d
0
       0
3
   402,888d
3
   9,541
The maximum variance is 34 days

1,154 YEAR SPANS
 14,273 months =   421,490d  4h   89p
 14,274 months =   421,519d 16h  882p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   421,488d
4
  10,136
-2
         0d
0
       0
-1
   421,489d
5
 202,079
-1
         0d
0
       0
0
   421,490d
6
  60,290
0
   421,519d
0
  59,030
1
   421,491d
0
 308,103
1
   421,520d
1
  11,433
2
         0d
0
       0
2
   421,521d
2
  37,346
3
         0d
0
       0
3
   421,522d
3
   1,055
The maximum variance is 34 days

1,174 YEAR SPANS
 14,520 months =   428,784d  5h  480p
 14,521 months =   428,813d 18h  193p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   428,782d
4
   6,545
-2
         0d
0
       0
-1
   428,783d
5
 114,993
-1
         0d
0
       0
0
   428,784d
6
  33,239
0
   428,813d
0
 195,240
1
   428,785d
0
 171,815
1
   428,814d
1
  36,520
2
         0d
0
       0
2
   428,815d
2
 124,662
3
         0d
0
       0
3
   428,816d
3
   6,458
The maximum variance is 34 days

1,194 YEAR SPANS
 14,767 months =   436,078d  6h  871p
 14,768 months =   436,107d 19h  584p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   436,076d
4
     866
-2
         0d
0
       0
-1
   436,077d
5
  25,222
-1
         0d
0
       0
0
   436,078d
6
   7,622
0
   436,107d
0
 333,645
1
   436,079d
0
  38,866
1
   436,108d
1
  64,185
2
         0d
0
       0
2
   436,109d
2
 210,437
3
         0d
0
       0
3
   436,110d
3
   8,629
The maximum variance is 34 days

1,252 YEAR SPANS
 15,485 months =   457,281d  6h    5p
 15,486 months =   457,310d 18h  798p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   457,279d
4
   6,214
-2
         0d
0
       0
-1
   457,280d
5
 166,556
-1
         0d
0
       0
0
   457,281d
6
  50,855
0
   457,310d
0
  92,155
1
   457,282d
0
 284,407
1
   457,311d
1
  19,055
2
         0d
0
       0
2
   457,312d
2
  66,396
3
         0d
0
       0
3
   457,313d
3
   3,834
The maximum variance is 34 days

1,272 YEAR SPANS
 15,732 months =   464,575d  7h  396p
 15,733 months =   464,604d 20h  109p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   464,573d
4
   2,184
-2
         0d
0
       0
-1
   464,574d
5
  86,586
-1
         0d
0
       0
0
   464,575d
6
  26,677
0
   464,604d
0
 222,749
1
   464,576d
0
 138,569
1
   464,605d
1
  43,081
2
         0d
0
       0
2
   464,606d
2
 156,894
3
         0d
0
       0
3
   464,607d
3
  12,732
The maximum variance is 34 days

1,323 YEAR SPANS
 16,363 months =   483,209d  2h  739p
 16,364 months =   483,238d 15h  452p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   483,207d
4
  14,557
-2
         0d
0
       0
-1
   483,208d
5
 150,703
-1
         0d
0
       0
0
   483,209d
6
  39,801
0
   483,238d
0
 167,095
1
   483,210d
0
 194,107
1
   483,239d
1
  29,958
2
         0d
0
       0
2
   483,240d
2
  92,854
3
         0d
0
       0
3
   483,241d
3
     397
The maximum variance is 34 days

1,343 YEAR SPANS
 16,610 months =   490,503d  4h   50p
 16,611 months =   490,532d 16h  843p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   490,501d
4
   4,117
-2
         0d
0
       0
-1
   490,502d
5
  55,216
-1
         0d
0
       0
0
   490,503d
6
  15,244
0
   490,532d
0
 320,204
1
   490,504d
0
  70,575
1
   490,533d
1
  53,396
2
         0d
0
       0
2
   490,534d
2
 167,626
3
         0d
0
       0
3
   490,535d
3
   3,094
The maximum variance is 34 days

1,350 YEAR SPANS
 16,697 months =   493,072d  7h 1001p
 16,698 months =   493,101d 20h  714p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   493,070d
4
   2,292
-2
         0d
0
       0
-1
   493,071d
5
 136,014
-1
         0d
0
       0
0
   493,072d
6
  43,081
0
   493,101d
0
 120,299
1
   493,073d
0
 254,069
1
   493,102d
1
  26,677
2
         0d
0
       0
2
   493,103d
2
  98,766
3
         0d
0
       0
3
   493,104d
3
   8,274
The maximum variance is 34 days

1,401 YEAR SPANS
 17,328 months =   511,706d  3h  264p
 17,329 months =   511,735d 15h 1057p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   511,704d
4
  12,308
-2
         0d
0
       0
-1
   511,705d
5
 208,595
-1
         0d
0
       0
0
   511,706d
6
  61,014
0
   511,735d
0
  60,659
1
   511,707d
0
 298,691
1
   511,736d
1
  11,433
2
         0d
0
       0
2
   511,737d
2
  36,260
3
         0d
0
       0
3
   511,738d
3
     512
The maximum variance is 34 days

1,421 YEAR SPANS
 17,575 months =   519,000d  4h  655p
 17,576 months =   519,029d 17h  368p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   518,998d
4
   8,174
-2
         0d
0
       0
-1
   518,999d
5
 118,251
-1
         0d
0
       0
0
   519,000d
6
  33,239
0
   519,029d
0
 200,670
1
   519,001d
0
 166,928
1
   519,030d
1
  36,520
2
         0d
0
       0
2
   519,031d
2
 121,042
3
         0d
0
       0
3
   519,032d
3
   4,648
The maximum variance is 34 days

1,428 YEAR SPANS
 17,662 months =   521,569d  8h  526p
 17,663 months =   521,598d 21h  239p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   521,567d
4
     490
-2
         0d
0
       0
-1
   521,568d
5
 174,206
-1
         0d
0
       0
0
   521,569d
6
  57,534
0
   521,598d
0
  33,646
1
   521,570d
0
 384,666
1
   521,599d
1
   7,622
2
         0d
0
       0
2
   521,600d
2
  28,702
3
         0d
0
       0
3
   521,601d
3
   2,606
The maximum variance is 34 days

1,441 YEAR SPANS
 17,822 months =   526,294d  5h 1046p
 17,823 months =   526,323d 18h  759p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   526,292d
4
   1,228
-2
         0d
0
       0
-1
   526,293d
5
  25,946
-1
         0d
0
       0
0
   526,294d
6
   7,622
0
   526,323d
0
 343,781
1
   526,295d
0
  37,780
1
   526,324d
1
  63,280
2
         0d
0
       0
2
   526,325d
2
 203,378
3
         0d
0
       0
3
   526,326d
3
   6,457
The maximum variance is 34 days

1,499 YEAR SPANS
 18,540 months =   547,497d  5h  180p
 18,541 months =   547,526d 17h  973p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   547,495d
4
   8,386
-2
         0d
0
       0
-1
   547,496d
5
 171,986
-1
         0d
0
       0
0
   547,497d
6
  51,217
0
   547,526d
0
  94,870
1
   547,498d
0
 276,443
1
   547,527d
1
  19,055
2
         0d
0
       0
2
   547,528d
2
  64,586
3
         0d
0
       0
3
   547,529d
3
   2,929
The maximum variance is 34 days

1,519 YEAR SPANS
 18,787 months =   554,791d  6h  571p
 18,788 months =   554,820d 19h  284p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   554,789d
4
   3,451
-2
         0d
0
       0
-1
   554,790d
5
  89,120
-1
         0d
0
       0
0
   554,791d
6
  26,677
0
   554,820d
0
 229,265
1
   554,792d
0
 134,768
1
   554,821d
1
  43,081
2
         0d
0
       0
2
   554,822d
2
 152,550
3
         0d
0
       0
3
   554,823d
3
  10,560
The maximum variance is 34 days

1,590 YEAR SPANS
 19,665 months =   580,719d  3h  225p
 19,666 months =   580,748d 15h 1018p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   580,717d
4
   4,841
-2
         0d
0
       0
-1
   580,718d
5
  56,664
-1
         0d
0
       0
0
   580,719d
6
  15,244
0
   580,748d
0
 329,435
1
   580,720d
0
  68,403
1
   580,749d
1
  52,310
2
         0d
0
       0
2
   580,750d
2
 161,110
3
         0d
0
       0
3
   580,751d
3
   1,465
The maximum variance is 34 days

1,597 YEAR SPANS
 19,752 months =   583,288d  7h   96p
 19,753 months =   583,317d 19h  889p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   583,286d
4
   4,464
-2
         0d
0
       0
-1
   583,287d
5
 140,358
-1
         0d
0
       0
0
   583,288d
6
  43,081
0
   583,317d
0
 124,100
1
   583,289d
0
 247,553
1
   583,318d
1
  26,677
2
         0d
0
       0
2
   583,319d
2
  96,232
3
         0d
0
       0
3
   583,320d
3
   7,007
The maximum variance is 34 days

1,617 YEAR SPANS
 19,999 months =   590,582d  8h  487p
 20,000 months =   590,611d 21h  200p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   590,580d
4
     389
-2
         0d
0
       0
-1
   590,581d
5
  59,506
-1
         0d
0
       0
0
   590,582d
6
  19,055
0
   590,611d
0
 254,091
1
   590,583d
0
 102,490
1
   590,612d
1
  52,233
2
         0d
0
       0
2
   590,613d
2
 187,226
3
         0d
0
       0
3
   590,614d
3
  14,482
The maximum variance is 34 days

1,668 YEAR SPANS
 20,630 months =   609,216d  3h  830p
 20,631 months =   609,245d 16h  543p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   609,214d
4
   9,803
-2
         0d
0
       0
-1
   609,215d
5
 121,509
-1
         0d
0
       0
0
   609,216d
6
  33,239
0
   609,245d
0
 206,100
1
   609,217d
0
 162,041
1
   609,246d
1
  36,520
2
         0d
0
       0
2
   609,247d
2
 117,422
3
         0d
0
       0
3
   609,248d
3
   2,838
The maximum variance is 34 days

1,675 YEAR SPANS
 20,717 months =   611,785d  7h  701p
 20,718 months =   611,814d 20h  414p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   611,783d
4
   1,757
-2
         0d
0
       0
-1
   611,784d
5
 182,170
-1
         0d
0
       0
0
   611,785d
6
  59,344
0
   611,814d
0
  34,732
1
   611,786d
0
 373,625
1
   611,815d
1
   7,622
2
         0d
0
       0
2
   611,816d
2
  27,978
3
         0d
0
       0
3
   611,817d
3
   2,244
The maximum variance is 34 days

1,688 YEAR SPANS
 20,877 months =   616,510d  5h  141p
 20,878 months =   616,539d 17h  934p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   616,508d
4
   1,590
-2
         0d
0
       0
-1
   616,509d
5
  26,670
-1
         0d
0
       0
0
   616,510d
6
   7,622
0
   616,539d
0
 353,917
1
   616,511d
0
  36,694
1
   616,540d
1
  62,375
2
         0d
0
       0
2
   616,541d
2
 196,319
3
         0d
0
       0
3
   616,542d
3
   4,285
The maximum variance is 34 days

1,746 YEAR SPANS
 21,595 months =   637,713d  4h  355p
 21,596 months =   637,742d 17h   68p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   637,711d
4
  10,558
-2
         0d
0
       0
-1
   637,712d
5
 177,416
-1
         0d
0
       0
0
   637,713d
6
  51,579
0
   637,742d
0
  97,585
1
   637,714d
0
 268,479
1
   637,743d
1
  19,055
2
         0d
0
       0
2
   637,744d
2
  62,776
3
         0d
0
       0
3
   637,745d
3
   2,024
The maximum variance is 34 days

1,766 YEAR SPANS
 21,842 months =   645,007d  5h  746p
 21,843 months =   645,036d 18h  459p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   645,005d
4
   4,718
-2
         0d
0
       0
-1
   645,006d
5
  91,654
-1
         0d
0
       0
0
   645,007d
6
  26,677
0
   645,036d
0
 235,781
1
   645,008d
0
 130,967
1
   645,037d
1
  43,081
2
         0d
0
       0
2
   645,038d
2
 148,206
3
         0d
0
       0
3
   645,039d
3
   8,388
The maximum variance is 34 days

1,844 YEAR SPANS
 22,807 months =   673,504d  6h  271p
 22,808 months =   673,533d 18h 1064p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   673,502d
4
   6,636
-2
         0d
0
       0
-1
   673,503d
5
 144,702
-1
         0d
0
       0
0
   673,504d
6
  43,081
0
   673,533d
0
 127,901
1
   673,505d
0
 241,037
1
   673,534d
1
  26,677
2
         0d
0
       0
2
   673,535d
2
  93,698
3
         0d
0
       0
3
   673,536d
3
   5,740
The maximum variance is 34 days

1,864 YEAR SPANS
 23,054 months =   680,798d  7h  662p
 23,055 months =   680,827d 20h  375p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   680,796d
4
   1,294
-2
         0d
0
       0
-1
   680,797d
5
  61,316
-1
         0d
0
       0
0
   680,798d
6
  19,055
0
   680,827d
0
 262,055
1
   680,799d
0
  99,775
1
   680,828d
1
  51,871
2
         0d
0
       0
2
   680,829d
2
 181,796
3
         0d
0
       0
3
   680,830d
3
  12,310
The maximum variance is 34 days

1,915 YEAR SPANS
 23,685 months =   699,432d  2h 1005p
 23,686 months =   699,461d 15h  718p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   699,430d
4
  11,432
-2
         0d
0
       0
-1
   699,431d
5
 124,767
-1
         0d
0
       0
0
   699,432d
6
  33,239
0
   699,461d
0
 211,530
1
   699,433d
0
 157,154
1
   699,462d
1
  36,520
2
         0d
0
       0
2
   699,463d
2
 113,802
3
         0d
0
       0
3
   699,464d
3
   1,028
The maximum variance is 34 days

1,922 YEAR SPANS
 23,772 months =   702,001d  6h  876p
 23,773 months =   702,030d 19h  589p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   701,999d
4
   3,024
-2
         0d
0
       0
-1
   702,000d
5
 190,134
-1
         0d
0
       0
0
   702,001d
6
  61,154
0
   702,030d
0
  35,818
1
   702,002d
0
 362,584
1
   702,031d
1
   7,622
2
         0d
0
       0
2
   702,032d
2
  27,254
3
         0d
0
       0
3
   702,033d
3
   1,882
The maximum variance is 34 days

1,935 YEAR SPANS
 23,932 months =   706,726d  4h  316p
 23,933 months =   706,755d 17h   29p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   706,724d
4
   1,952
-2
         0d
0
       0
-1
   706,725d
5
  27,394
-1
         0d
0
       0
0
   706,726d
6
   7,622
0
   706,755d
0
 364,719
1
   706,727d
0
  35,608
1
   706,756d
1
  60,804
2
         0d
0
       0
2
   706,757d
2
 188,594
3
         0d
0
       0
3
   706,758d
3
   2,779
The maximum variance is 34 days

1,942 YEAR SPANS
 24,019 months =   709,295d  8h  187p
 24,020 months =   709,324d 20h  980p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   709,293d
4
   1,378
-2
         0d
0
       0
-1
   709,294d
5
 114,502
-1
         0d
0
       0
0
   709,295d
6
  36,520
0
   709,324d
0
 158,099
1
   709,296d
0
 210,480
1
   709,325d
1
  33,239
2
         0d
0
       0
2
   709,326d
2
 124,137
3
         0d
0
       0
3
   709,327d
3
  11,117
The maximum variance is 34 days

1,993 YEAR SPANS
 24,650 months =   727,929d  3h  530p
 24,651 months =   727,958d 16h  243p
M'+/-DAYSMOD 7dOCCURSM"+/-DAYSMOD 7dOCCURS
-2
   727,927d
4
  12,730
-2
         0d
0
       0
-1
   727,928d
5
 182,846
-1
         0d
0
       0
0
   727,929d
6
  51,941
0
   727,958d
0
 100,300
1
   727,930d
0
 260,515
1
   727,959d
1
  19,055
2
         0d
0
       0
2
   727,960d
2
  60,966
3
         0d
0
       0
3
   727,961d
3
   1,119
The maximum variance is 34 days


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For other Additional Notes click here.
Hebrew Calendar Science and Myths

I'd love to hear from you. Please send your thoughts to:

Remy Landau

First  Paged 30 Jul 2001
Next Revised  9 Aug 2001