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Originally Posted by eepiccolo

First, let's note that the sentence begins with "Looking at past factoring data we see that the chance ..." Right now I don't recall whether I've seen a proof of that estimate. Judging by the sentence's wording, it may be an empirical observation.
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My question is this: is this probability dependent or independent of whether or not other factors have been found?

If I understand correctly, what is meant is "... the chance that 2^p1 has a factor between 2^x and 2^(x+1) is approximately 1/x."
That is, it refers to the probability of the existence of a factor (known or unknown) of 2^p1 within the specified range, not necessarily the probability of discovering a previouslyunknown factor there after some factors of 2^p1 are already known.