Is everybody a decendent of the Prophet Muhammad [pbuh]?

I just read an interesting site on the internet. Working on the logic that the number of ascendents each human being has is 2^x [where x = number of generations back, since we each have 2 parents, 4 grandparents, 8 gt grandparents, 16 gt gt grandparents, 32 gt gt gt grandparents], that means that going back say 1000 years, each person has potentially billions of ancestors.

As an example, the furtherest ancestor I know about died in 1491 [in Gloustershire, England incidently]. That is 18 generations back from my daughter. Presumably, that means she has 262,144 eighteenth generation ancestors in total. Sure, some of them might be the same people, but let's hope not too many!

This of course is a little over 500 years ago. Now, what if we keep going back to around 900 CE? That means [for instance] 2³⁶ [36 generations back] she has a total of 68,719,476,736 36th generation ancestors. 68 billion!

Since there were only a fraction of that many people alive in 900 CE, we can assume that there were obviously some shared ancestors. However, given the laws of probability, it would be almost impossible that everybody in Europe [at least] is not related to each other in some way.

This is explained best at:
http://www.oz.net/~lee/Genealogy/charlemagne.html

Given that known descendents of the Prophet [PBUH] were living in Spain at that time, well... The point is that if you look throughout the Muslim world and even areas where Muslims / Christians interacted, it would be highly unlikely if the overwhelming majority of people do not have a genetic link to the sahabat [companions] and even to the Prophet Muhammad himself!

The question is then, what is the meaning of a title like 'Syed' in this day and age?

This all seems pretty convincing to me, with my limited maths. But if anyone has a different point of view, please explain!