# Are there any known languages in the intersection of NP and co-NP but not in P? [closed]

We currently don't know the relationship between NP and co-NP, but would it be possible to show whether the intersection is equal to P? I can't think of any languages in both NP and co-NP, but not in P.

• Note that you can't prove that any NP problem is outside of P as that would imply that P != NP Feb 13 '19 at 13:13

Proving that $$P= NP \cap$$ co-$$NP$$ is an open problem and believed to be unlikely since Integer factoring decision problem is in both $$NP$$ and co-$$NP$$ but conjectured to be outside $$P$$.