# Rarest calendar year

There are many variables in a jewish calendar year, so for the purpose of my question, I'm asking for the rarest confluence of "days of the week" with significant calendar dates (to determine what significant means, let's say days that we don't say tachanun). So for example, for Rosh Hashana to occur on a monday, Hannukah on a Shabbat, Tu B'shvat to occur on a Wednesday, Purim on a Thursday... and so on may be the rarest combination.

(If I'm not mistaken, this question should be Israel/Diaspora agnostic.)

Bonus question: when did this year last occur and when will it occur next?

• Yom Ha'atzmut is up to the responder to decide ;) Commented Jul 27 at 22:19
• 355-day year starting on Thursday Commented Jul 28 at 1:37
• Jewish calendar has 19 year moon cycle and 28 year solar cycle when everything comes to the same day of the week. 19 and 28 are relatively prime, so every 532 =19×28 years we should get a repetition. I.e. had the calendar been infinite - everything might average out. We believe that the calendar is 6000 years. Thus definitely it makes sense to ask, which occurence is the rarest and actually compute it!
– Y DJ
Commented Jul 28 at 3:29
• @DoubleAA which we will have this coming year (5785) Commented Jul 28 at 3:40
• @YDJ That's not how it works. The calendar almost repeats every 247 years, but the actual length of the cycle is 689,472 years. hebrewcalendar.tripod.com/#19 Commented Jul 28 at 6:33

As noted by DoubleAA in a comment, the rarest of the 14 possible types of year in the Hebrew calendar, is a 355-day year (i.e. a regular 12-month year, with both Marcheshvan and Kislev having 30 days) starting with Rosh HaShanah on a Thursday.

This year-type can be referred to as הש"א (that is ה - Rosh HaShanah is Thursday, ש (=שלמה) - Marcheshvan and Kislev have 30 days, א - first day Pesach is Sunday).