My feeling is that you are correct that the prime factorization is a red-herring for the reasons I mentioned in another post in this thread (solving the problem using that info is probably NP hard.) However, finding any nontrivial factor of a large number may be just as hard. Clearly, if one could do that in a reasonable time, then one could also find the prime factorization in a reasonable time. This would upset many people so much that I believe it is forbidden to publish any such result...even partial ones!! (Such results would defeat many common encryption schemes.)
chas
(***This was supposed to be in reply to BrowserUk's 432772 post,but it didn't seem to appear in the right position...likely something I did wrong...)

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