I just think this is interesting, so I am examining it a bit further.
- For a baby boy, there are 7 days of tumah, and then 33 days of dam tohar, total of 40 days.
- For a baby girl, there are 14 days of tumah, and then 66 days of dam tohar, a total of 80 days.
- Grand total 21 days of tumah, 99 days of dam tohar, 120 days total.
Why add them together? Because history also brings perfection to the male and the female sides.
If the 6000 years of history is divided up in to 120 days total, each day is 50 years.
- 21 * 50 = 1050 years of tumah
- 99 * 50 = 4950 years of dam tohar
We therefore have 1050 years to "fix", so to speak. This Tikkun is done by the Beit HaMikdash in Yerushalayim.
- Bayit Rishon stood 410 years.
- Bayit Sheini stood 420 years.
- 410 + 420 = 830 years total.
- 1050 - 830 = 220.
We have 220 years remaining that need to be fixed.
- 6000 - 220 = 5780
According to 1 opinion (I believe in the Rishonim, see the mefarshim to Rambam Hilchot Shemitah v'Yovel chapter 10), the 2nd Beit HaMikdash stood for 421 years.
- 6000 - 219 = 5781
But really, Adam HaRishon, who marks the beginning of the Era of Tikkun, was born in year 2, so we should add another year, since we should have 6000 years to make the Tikkun.
- 6001 - 219 = 5782