GENEALOGY n. The tracing of descent from ancestors; alternatively, a particular account of such tracing for a specific individual or family. In the English-speaking world, all those who take up this pursuit announce sooner or later that they can trace their descent back to Edward III. This should surprise no one with a rudimentary knowledge of mathematics; there are probably one or two well-bred basset hounds who could also trace their descent back to Edward III. What is really surprising is that Edward III seems to be regarded as some kind of ultimate antecedent beyond whom the genealogist does not venture, even though anyone descended from Edward III is also descended from his father Edward II, and so on. The author can guess only that the prudery of the late Victorian age (when genealogy became a family pastime) chose to draw a veil before the memory of Edward II in view of the sybaritic Plantagenet’s bisexual reputation and appalling death (see impalement).— Peter Bowler, The Superior Person’s Book of Words.
Interesting quote. I think anyone who taps into a royal line can ultimately go back to the earliest traceable ancestors of Charlemagne, the Arnulfings (descendants of Arnulf, bishop of Metz in the early 600s).
Anyone who can reliably trace ancestry back to Muhammad could then follow his ancestry back several generations earlier. There may be some Irish genealogies that are slightly older, and there are people today who claim descent from Confucius--if accurate, those lineages would be much longer.