This question remindes me of the news item that's been posted on the homepage of Eric Weisstein's MathWorld for a number of months:

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A paper submitted by P. Mihailescu on April 18 [2002] allegedly proves Catalan's 158-year-old conjecture.
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Am I right that this is the conjecture that the only positive integral powers of 2 and 3 that differ by 1 are 3 - 2 = 1 and 9 - 8 = 1 ???

Does anyone know whether this proof has been accepted by experts?  If so,  can  someone please give a sketch of the proof?

Thanks,

Dan