How was the Hebrew leap year distribution of 3 5 8 11 14 16 19 different than the currently used distribution of 3 6 8 11 14 17 19?

Admittedly, the leap year distribution 3 5 8 11 14 16 19 does indeed look different than the current distribution of 3 6 8 11 14 17 19. However, these two leap year distributions are exactly the same.

Examining the differences between the years in both of these cycles, we get 2 3 3 3 2 3 3 for the first cycle, and 3 2 3 3 3 2 3 for the second cycle. These two chains of numbers are circularly the same, as can be seen when the last number in each is then followed once again by the first number.

The actual diffference between these two 19 year distribution lies in the year counting method used.

The leap year distribution GUChADZaT is used for a Hebrew year counting system in which the beginning of each 19 year cycle is defined as 19 * M + 1.

The distribution 3 5 8 11 14 16 19 is used for a Hebrew year counting system in which the beginning of each 19 year cycle is defined as 19 * M - 2.

The modulo 19 difference between these 2 year counting systems is -3. So, if you subtract 3 from each of the years in the leap year cycle 3 6 8 11 14 17 19 (GUChADZaT), you derive
0 3 5 8 11 14 16.

Since 0 is 19 modulo 19, the number 19 can be substituted for 0, giving us
3 5 8 11 14 16 19. Hence, both leap year distributions are exactly the same.

Assuming 13 Hebrew years, what is the oldest that a bar/bat mitzvah celebrant can be on their 13th birthday?

The longest period of 13 Hebrew years, as measured from the first day of Tishrei is 4756 days. Therefore, that would be the oldest possible age in days for a 13 year old.

In the full Hebrew calendar cycle of 689,472 years, these periods of 4756 days occur 54,347 times.

Correspondent Larry Padwa sent the following observations

Every 13 year period has at least four and at most five leap years. For the person to be has old as possible, there should be five leap years between birth and age 13, giving an answer of 161 months.

Further analysis (which I haven't done) can be used to determine how many of the thirteen years can be deficient, normal, or abundant in order to maximize the number of days in the thirteen year interval.

Thank you Larry. It is to be hoped that you will try to solve the charming puzzle you recognized with regards to the number of days.

Will the Gregorian 21st century begin on January 1, 2000g?

YES!

And that date will also mark the first day of the third millenium in the Gregorian calendar.

The argument used to refute these assertions is that the Julian calendar went from the year 1 bce to the year 1 ce skipping the year zer0.

However, the argument cannot and does not apply to the Gregorian calendar. The first date of the Gregorian calendar was Friday 15 October 1582g, corresponding to 19 Tishrei 5343H
(the 5th day of the Hebrew festival of Sukkot 5343H).

Therefore, NO Gregorian date prior to October 15, 1582g has ever existed, and therefore, noone can provide any factual basis for suggesting that the Gregorian calendar began the common era with the year 1g instead of the year 0g.

The only way of extending the Gregorian calendar prior to October 15, 1582g is through the method of mathematical induction. In this way, a set of virtual dates can be created which can and does include the year 0g.

Scientists and mathematicians assume the existence of the year 0g and treat it as as a Gregorian leap year. This assumption is also made in Hebrew Calendar Science and Myths.

When will the next millenium start in the Hebrew calendar?

The Hebrew calendar is presently using a system of year counting known as the
World Era (Aera Mundi). The start of that era is the Hebrew year 1H (Mon 7 Sep -3760g).

Since the current World Era year is 5759H, the next millenium in the Hebrew calendar will begin Rosh Hashannah 6001H which corresonds to Thursday 17 September 2240g.

The year 6001H (2240g/1g) will be a 355 day year. Quite surprisingly, 17 Sep 2240g will be the last time for many thousands of years that any Hebrew non-leap year will begin on that date.

When will the next Hebrew non-leap year begin on September 17 after the year 2240g?

It is assumed for purposes of discussion that no changes will take place to either the Hebrew or the Gregorian calendars over the indicated time spans.

The last Hebrew non-leap year to start on September 17 will be in the year 2240g. For several thousands of years after that, no 12-month Hebrew year will occur on that date.

Hebrew leap years, on the other hand, will continue to coincide with September 17 until
Sat 8605H (4844g).

The first day of Tishrei will then no longer coincide with September 17 until
Mon 86,060H (82,300g). That date will then also mark the start of the first 12-month Hebrew year since the year 2240g.

In days, how long can be any period or cycle of 247 Hebrew years?

Periods of 247 Hebrew years can be either 90214, 90215, or 90216 days long.

These periods occur at the rate of 1.5%, 0.5%, and 98% of the time respectively.

Since the longest of the 247 year periods is an exact number of weeks, and occurs most of the time, it was once felt that the 247 period represented the full Hebrew calendar cycle.

When did the least frequently occurring 247 Hebrew year period last begin?

Periods of 247 Hebrew years can be either 90214, 90215, or 90216 days long.

These periods occur at the rate of 1.5%, 0.5%, and 98% of the time respectively. Hence, the 90215-day period is the least frequently occurring period of 247 years.

The 90,215-day period of 247 Hebrew years occurs only 3,439 times in the full Hebrew calendar cycle of 689,472 years.

This period of time last began on Tue 27 Sep 1927g (5688H).

What's the smallest number of consecutive Hebrew years that cannot add up to a whole number of weeks?

The smallest number of Hebrew years that cannot add to a whole number of weeks is 8.

1             Hebrew year       can have  385 days which is  55 weeks.
2 consecutive Hebrew years      can have  707 days which is 101 weeks.
3 consecutive Hebrew years      can have 1092 days which is 156 weeks.
4 consecutive Hebrew years      can have 1449 days which is 207 weeks.
4 consecutive Hebrew years also can have 1477 days which is 211 weeks.
5 consecutive Hebrew years      can have 1799 days which is 257 weeks.
6 consecutive Hebrew years      can have 2184 days which is 312 weeks.
7 consecutive Hebrew years      can have 2541 days which is 363 weeks.
7 consecutive Hebrew years also can have 2569 days which is 367 weeks.

However, 8 consecutive Hebrew years do not have a single length that is formed from a whole number of weeks.

Of all of the lengths possible for 8 consecutive Hebrew years, the shortest of these is 2,892 days long and it only occurs 9 times in the full 689,472 year cycle of the Hebrew calendar.

When did, or will, occur the first of the shortest consecutive 8 Hebrew year periods?

The smallest number of consecutive Hebrew years that cannot add to a whole number of weeks is 8.

Periods of 8 Hebrew years can be either 2892, 2893, 2894, 2895, 2922, 2923, 2924, or 2925 days long.

Of all of the lengths possible for 8 consecutive Hebrew years, the shortest of these is 2,892 days long and it only occurs 9 times in the full 689,472 year cycle of the Hebrew calendar.

Assuming no changes to either the Hebrew or the Gregorian calendars, then the first time that this shortest period of 8 years will begin is on Monday Rosh Hashannah 114788H
(19 Jan 111029g).

Correspondent W. Gerum sent the following correct answer

Shalom, may you live until Jan, 19 111029 to celebrate Rosh Hashannah 114788 which happens to be the beginning of the earliest of the shortest 8-year periods

baruch ha-Shem

Good work W. Gerum! Thank you! And may you also be there to email a Shannah Tovah!

The period of the molad is 29d 12h 793p which is a bit over 29 and a half days, and a bit under 30 days, corresponding to about 29.5306 days.

Since the period of the molad is less than 30 days, is it possible for the molad to occur beyond the 30th day of a Hebrew month?

The answer raises a number of apparent paradoxes and may have been one of the major reasons behind the formulation of the 2 day observance of Rosh Chodesh.

Although the period of the molad is less than 30 days, it is possible for a molad to make its appearance beyond the 30th day of some Hebrew months.

Instantly, as shown by the considerations of the Overpost Problem in the Additional Notes, it is possible to realize that the molad can never occur 30 days after the first day of deficient months. If that were the case, then the molad would come after the first day of some months.

However, the molad can arrive 30 days after the first day of full months. Such days would be the first days of the subsequent new month.

Under no circumstance is it ever possible for the molad to arrive 31 days after the first day of any Hebrew month.

Calendar arithmetic shows that the molad can occur 30 days after the first day Tishrei, Kislev, Shevat, Adar I, Nisan, Sivan, and Av.

In abundant years, only the month of Heshvan can, in some years, have its molad occur on the 31st day of its predecessor month of Tishrei.

The phenomenon of a molad on the 31st day of its preceding month does not occur in every Hebrew year.

 First  Begun 21 Jun 1998 
First  Paged  5 Nov 2004
Next Revised  5 Nov 2004