"necessarily not" is correct and usable in written English.
You can use it when you want to emphasize that something is definitely not true. For example: "You don't necessarily need to go out to have fun - you can just stay home and watch a movie."
Not a glitch, necessarily, not a ding, but a something.
Not necessarily — not for many of us, and not for much of American history.
The son would have to fit in at Oxford, but necessarily not be among the cream of the applicants, and would be given a 'guaranteed entry'.
It should be regarded "not as a one-time thing and not necessarily not as a one-time thing," he said.
"To be a good artistic director, you don't necessarily not have to have an ego, but you have to love artists," said one artistic director who spoke on the condition of anonymity .You have to love artists other than yourself".
But you could just as easily say that the kind of person capable of being the greatest distance runner of his generation is necessarily NOT going to look like you and me.
He sums up his conclusions about change and generalizes to other kinds saying: "And so necessarily not-being applies to (epi) change and to (kata) all the other kinds" (Sophist 256d); and then: "So about (peri) each of the forms the being is much and the not-being is unlimited in multitude" (Sophist 256e).
"Not necessarily, or not quite..
Normally, "possibly P" is taken to be equivalent to "not-necessarily not-P", and "necessarily P" is taken to be equivalent to "not-possibly not-P".
This view would also run into difficulties if we retain the standard interdefinition of "necessarily P" with "not-possibly not-P" and "possibly P" with "not-necessarily not-P".
Not necessarily: correlation does not imply causation.
