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As well as implying NP=co-NP, it would also imply that BQP contained NP.

It would also seem to imply that hard instances of NP-complete problems were easy to generate.

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Since integer factorization is known to be in both NP and co-NP, a proof that it is NP-complete would imply NP = co-NP, which is considered highly unlikely.

There is an interesting discussion at this old post by Lance Fortnow.

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