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primality testing is a poor example. PRIMES is in P.

http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v...



Even factoring would be a poor example, given that it has never been shown to be NP-complete.


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.




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