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You have yet to show that the Bible claims that the Earth is x number of years old. I saw exactly one source on this, which was the website where one guy tried to extrapolate a chronology from the Bible. The Bible makes no claim as to the exact moment of the beginning of mankind. Its really that simple.
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Adam to Noah: 874 years, Genesis 5
Noah to Abraham: 790, Genesis 11
55 more generations to Christ. I'll even be generous and give you 40 years between generations. Another 2,200.
Genealogy
Total: 3,864 BC, 2005 after = 5,869.
Your book appears to have at least one glaring error.