In the Christmas story, King Herod the Great was depicted as a despot king. However, his estimated date is useful to narrow estimated year of Christ birth, because Christ was born when Herod the great was alive. Josephus, a secular Jewish historian living in 1 AD century narrated the death of King Herod the Great.

In his book, Josephus recounted that Herod had reign for 37 years since he had been made king by the Romans and 34 years since he had caused Antigonus to be slain.
So Herod, having survived the slaughter of his son five days, died, having reigned thirty-four years since he had caused Antigonus to be slain, and obtained his kingdom; but thirty-seven years since he had been made king by the Romans.1
Calculation since he had been made king by the Romans:
Herod reign | BCE |
1st year | 40 |
2nd year | 39 |
3rd year | 38 |
4 | 37 |
5 | 36 |
6 | 35 |
7 | 34 |
8 | 33 |
9 | 32 |
10 | 31 |
11 | 30 |
12 | 29 |
13 | 28 |
14 | 27 |
15 | 26 |
16 | 25 |
17 | 24 |
18 | 23 |
19 | 22 |
20 | 21 |
21 | 20 |
22 | 19 |
23 | 18 |
24 | 17 |
25 | 16 |
26 | 15 |
27 | 14 |
28 | 13 |
29 | 12 |
30 | 11 |
31 | 10 |
32 | 9 |
33 | 8 |
34 | 7 |
35 | 6 |
36 | 5 |
37 | 4 |
Calculation since he had caused Antigonus to be slain:
Herod reign | BCE |
1st year | 37 |
2nd year | 36 |
3rd year | 35 |
4 | 34 |
5 | 33 |
6 | 32 |
7 | 31 |
8 | 30 |
9 | 29 |
10 | 28 |
11 | 27 |
12 | 26 |
13 | 25 |
14 | 24 |
15 | 23 |
16 | 22 |
17 | 21 |
18 | 20 |
19 | 19 |
20 | 18 |
21 | 17 |
22 | 16 |
23 | 15 |
24 | 14 |
25 | 13 |
26 | 12 |
27 | 11 |
28 | 10 |
29 | 9 |
30 | 8 |
31 | 7 |
32 | 6 |
33 | 5 |
34 | 4 |
These tables show that Herod the Great died in 4 BCE according to Josephus account.

Josephus recounted that King Herodes the Great died between 2 lunar eclipse. In 4 BCE, lunas eclipse occured on March 13 and September 5. Then, King Herod the Great died between March and September 4 BCE.
Conclusion
Herod died not less than March 13, 4 BCE, then:
- Jesus born before March 13, 4 BCE.
- Qirinius hegemonized Syria between 5-4 BCE. It implies that Qirius was a duumvir with Varus.
Bibliography
1http://www.ccel.org/j/josephus/works/war-1.htm ; akses 20/3/2015 16:47
2http://www.ccel.org/j/josephus/works/ant-17.htm ; akses 20/3/2015 17:17
3http://www.reuters.com/article/2008/11/19/us-israel-archaeology-idUSTRE4AI7S920081119 ; akses 20/3/2015 18:02
4http://www.itsgila.com/highlightsherodion.htm ; akses 20/3/2015 18:08
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