Probably, almost all of them.
A couple of days ago, Victor Mair wrote about some provocative behavior on the part of "Kŏng Qìngdōng 孔庆东, associate professor in the Chinese Department at Peking University, who also just happens to be the 73rd generation descendant of Confucius (Kǒng Fūzǐ 孔夫子 ; Kǒng Qiū 孔丘), or at least he claims to be a descendant of Confucius." . . .
[In numerical geneological models there was] a threshold, let us say Un generations ago, before which ancestry of the present-day population was an all or nothing affair. That is, each individual living at least Un generations ago was either a common ancestor of all of today's humans or an ancestor of no human alive today. Thus, among all individuals living at least Un generations ago, each present-day human has exactly the same set of ancestors. We refer to this point in time as the identical ancestors (IA) point. . . .
Within China, there's been more than enough mixing to ensure that by now, if anyone is a descendent of Confucius, everyone is.
The date for a most recent common ancestor of all members of a population by any line of descent is generally (and logically) considerably more recent than the identical ancestor point.
Also, realistically, there is enough non-randomness and structure in human reproductive choices that "almost everyone is" to a very high percentage figure (perhaps 99.999%+) is probably quite more likely to be the case than literally "every single person is." There might be only 12,000 people or less in China who are not descended from Confucius at all, but in real life, there are probably some people who are not.
An exploration of the kind of assumptions one has to make to reach these conclusions is explored in the linked post. Suffice it to say that the results are quite robust with range of numerical values for assumptions in population models that is much broader than intuition would suggest producing similar historical points at which all persons in a population have a shared common ancestors and an identical set of ancestors (not necessarily in the same proportions) respectively.
I have not quoted an estimate in the original post regarding the likelihood that someone in China has a least one of their genes derived from Confucius because, as pointed out in the comments to that post, the estimate is profoundly wrong.
The actual probability that a Han Chinese person has a gene derived from Confucius from some ancestor is actually on the order of 2.5% (assuming that there are about 25,000 genes in humans) not "3 chances in a quintillion" as the original post claims, because the original post ignores that fact that most people will have multiple lines of descent to the same historical person. But, the underlying point, that having someone in your geneology does not necessarily mean that you have any genetic descent from them several dozen generations later, is a valid point.
As a footnote, the increasingly strong possibility that most people in a large population will have multiple lines of descent (indeed a great many multiple lines of descent) to most or all of the total set of people who are ancestral to the current population, is very much the same kind of observation that makes it heuristically very likely that Goldbach's Conjecture is true for all very large numbers.
The identical ancestor point has some very practical implications for population genetics. For example, the closed set of ancestors implies that, with the exception of mutations that have happened since the identical ancestor point and managed to remain in the gene pool, that the set of genes present in someone in the population is closed at the IA date.
The way the numbers work out, a population that isn't fully isolated from another population is typically going to have an IA date that is certainly within the Holocene era (i.e. about twelve thousand years ago) and typically somewhere within the historic era (i.e. about six thousand years ago). Of course, sustained periods of complete isolation of different populations from each other pushes the IA date back to sometime before the populations were separated. But even slight amounts of population exchange for a surprisingly small number of generations can dramatically reduce the time frame in which everyone in two populations have a most recent common ancestor or identical ancestors.
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