Is Integer Factorization Harder Than RSA Factorization?

Is the prime factorization problem in NP class? If not, supposing P = NP, would  RSA encryption and other such  algorithms which rely on prime factorization being hard be rendered ineffective?

• Answer:

  The prime factorization problem is in the NP class, but we don't know if it is NP-hard. In other words, there is currently no proof that prime factorization problem cannot be solved polynomial time (= in P). Subsequently there is no proof that algorithms that rely on prime factorization being hard be rendered ineffective. As a side note, on a quantum computer, to factor an integer N, http://en.wikipedia.org/wiki/Shor%27s_algorithm runs in polynomial time. More details at http://en.wikipedia.org/wiki/Integer_factorization#Difficulty_and_complexity.