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THREE SCORE AND TEN is the nominal span of a human life — 3 x 20 + 10.
In the days that this expression was coined that span was considered to be 70 years.

"The days of our years are threescore years and ten." [The Bible, KJV, Psalms 90:10]

'Threescore' used to be used for sixty, in the way that we still use a dozen for twelve, and (occasionally) score for twenty. 

"He had lived for threescore years and ten."

The connecting notion probably is counting large numbers (of sheep, etc.) with a notch in a stick for each 20. That way of counting, called vigesimalism, also exists in French.* 

"I hope I do half as much as my grandpa's done by the time I'm threescore and ten."

The use of 'threescore' as a name for sixty has long since died out but is still remembered in this phrase. Threescore goes back to at least 1388, as in this from , at that date:

"Thre scoor and sixe daies." [John Wyclif's Bible, Leviticus 12]

As with many other Biblical phrases, this was picked up by Shakespeare. 

"Threescore and ten I can remember well." [Macbeth, 1605]

It's an odd fact that, although Shakespeare took numerous phrases and examples of imagery from the Bible, the word 'Bible' doesn't appear in any of his plays.

* In Old French, "twenty" (vint) or a multiple of it could be used as a base, as in 'vint et doze' (32), 'dous vinz et diz' (50). Vigesimalism was or is a feature of Welsh, Irish, Gaelic and Breton (as well as non-IE Basque), and it is speculated that the English and the French picked it up from the Celts. Compare 'tally' (n.).

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