Even factoring would be a poor example, given that it has never been shown to be NP-complete.
Re:An Argument for P=NP (2005) [pdf]
by BrainInAJar on Monday August 17, 2015 @04:32PM
(#10075906)
It would be very surprising if it were, since it's also in co-NP. The other problems in NP intersect co-NP are all in P. It's not at all unlikely, and a lot of evidence points towards, that integer factorization is in P.
http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v...