The chronology on which our calendar is based uses an assumption:
The first year of a life is year 0. In other words, we count the number of birthdays completed.
Using this assumption, we can arrive at all the traditional dates, that the Flood was in 1656, that Avraham was born in 1948, that the Exodus was in 2448, etc. The problem is with the birth of Adam HaRishon.
In order to get the traditional dates, Adam HaRishon must be born in year 0. This is problematic:
- Birkat HaChamah is based on the creation of the sun being in Nissan of year 1 (according to the opinion that Creation was in Nissan), which is why the formula for Birkat HaChamah is 1 + 28n, for 0 <= n <= 214. According to this, we should say Adam HaRishon was born in year 1 (in Nissan)
- The Molad that we calculate today is based on the 1st day of Creation being the 25th of Elul, year 1 (according to the opinion that Creation was in Tishrei). In other words, Adam HaRishon is born on Rosh Hashanah of year 2.
According to the above, our chronology of Adam HaRishon being born in year 0 indicates that the 2nd Beit HaMikdash was destroyed in 3828. Yet according to the other systems of counting, we could say that it was destroyed in 3829 or 3830.
There is a statement I believe in a few places, including the Zohar Chadash, that says that the 2nd Beit HaMikdash was destroyed in the year after Shmitah. Shmitah, according to our counting, is any year evenly divisible by 7 (like this year, 5768, is evenly divisible by 7 a total of 824 times). This would make 3830 the closest year that mathematically fits this statement. However, it is not necessary to fit this, because Shmitah (I believe according to most opinions, correct me if I am wrong) was counted by the Sanhedrin during the 2nd Beit HaMikdash period, meaning it wasn't based on the overall year count (where a Shmitah Year is when year divided by 7 is an integer).
The idea that Adam HaRishon was born in year 0, according to this counting system, has a message that the 6000 years that we count is really the 6000 year life of Adam HaRishon, and not just the world overall. It is a 6000 year story of the development of mankind.