Speaking pedantically, P is in NP also. I suspect that NP is being used as shorthand for NP-complete, not just NP. As for actual deterministic factorization Wikipedia says that
'It is suspected to be outside of all three of the complexity classes P, NP-complete, and co-NP-complete'
So even if this showed 'P = NP-complete' it may not imply imply factorization is in P. I'm at the limits of my rusty complexity knowledge here so if any knows better please correct me.
'It is suspected to be outside of all three of the complexity classes P, NP-complete, and co-NP-complete'
So even if this showed 'P = NP-complete' it may not imply imply factorization is in P. I'm at the limits of my rusty complexity knowledge here so if any knows better please correct me.