It's Also About the Tekufah

Birkat HaChamah is when the Tekufat Nissan moment falls in the beginning of the night on the 4th day of the week.

In the year of Yetziat Mitzraim (2449), Tekufat Nissan fell on the first hour of Thursday, which is when Yetziat Mitzraim took place.  I don't have a method handy to check if that was the middle of the lunar month to actually be the 15th of Nissan.

• In the year of Binyan Bayit Rishon (2929), Tekufat Nissan fell on the first hour of Tuesday.
• In the year of Nes Purim (or perhaps the year before), Tekufat Nissan was also on the first hour of Tuesday.
• In the year of Binyan and Churban Bayit Sheini (3409 and 3829 respectively), Tekufat Nissan fell on the first hour of Sunday (and our tradition likewise states that the Churban was on a Saturday night).

Anyone that wishes to take a look can set up an Excel spreadsheet with the following formulas:

• Column A start at 1 and A2=A1+1, etc.
• Column B starts at 73 (Tekufat Nissan at the 73rd hour of the week is the beginning of Tuesday night).  Subsequent cells should be as follows: B2=MOD(B1+30,168), because each year, the Tekufah is 30 hours later, and the week has a total of 168 hours.
• Column C starts at 1.  Subsequent cells should be as follows: C2=If(C1=4,1,C1+1), so that will give you a count to 4, where if the row = 1, the Tekufah is the beginning of the night.

The Tekufah moment for 5727 and 5783 is identical, since they are a multiple of 28 years apart.