How far back does one need to go until, in your opinion, a segment from a shared ancestor becomes largely irrelevant?

I mean if one shares a segment of DNA with a 14th cousin from a 16th century ancestor, does not the sheer distance and greatly reduced size of population back then make this shared DNA virtually indistinguishable from the general population?

I'm reminded of the theory, based on mathematical probability, that virtually every European is descended from Charlemagne. What of genetic matches from later on but still a long time ago, such as 500 years back?

I mean if one shares a segment of DNA with a 14th cousin from a 16th century ancestor, does not the sheer distance and greatly reduced size of population back then make this shared DNA virtually indistinguishable from the general population?

I'm reminded of the theory, based on mathematical probability, that virtually every European is descended from Charlemagne. What of genetic matches from later on but still a long time ago, such as 500 years back?

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