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Originally Posted by polyestr
Question: Imagine a computer has a hardware defect that is exposable through prime95's torture test. Is the probability of the torture test exposing this defect by failing a test the same in a 20hour run as it is in two 10hour runs?

Well, that may depend on the exact nature of the defect, but I'll guess that, in general, a 20hour run is slightly more stressing (and thus slightly more likely to expose the defect) than two 10hour runs. For example, heat buildup  running it continuously for a whole day, including the period when the system's surroundings are diurnally warmest, is better than a series of runs that miss the heat of the day. (But two runs during the hottest 10 hours of each of two days might be more stressing than one 20hour run that includes only one complete daily hot period.)
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I guess what I'm asking is whether the tests progressively "focuses in" in any way,

Not really
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or if each test is simply an independent event.

Basically, yes.
A torture test runs a certain number of LL iterations on each of many different exponents (actually, Mersenne numbers with different exponents, of course). The table of test exponents (and the corresponding correct answer for each one) is fairly long  many dozens of different exponents, covering a wide range. I think it may take more than 24 hours to cycle through the complete set of test exponents on at least some systems, so letting the torture test run for long periods is the best way to push as many different bit patterns through as possible, so as to maximize the probability of hitting upon a pattern that is defectively processed.