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ROB said, ” there is still the matter of a 166-year gap (from 586 to 420)that is in conflict with other historical records. “
The only explanation that I heard to be machria is that the Galut ended after 70 years, but that it took a very long time (165 more years) until Bayit Sheni was built. If you want to say that, you have to say that we are in year 5939 (5774 + 165), not 5774.
Here’s my math: assuming 586 BCE is when Bayit Rishon was destroyed, and in 351 BCE Bayit Sheni was built, that’s 235 years. 70 years of Galut. That leaves 165 years where the Jews were in their land, but not with a Temple.