>>1
No. And as a bonus, here is a proof which doesn't require an "infinity is not a number, etc, proof".
(1) By definition, a prime number is in the set of natural numbers.
(2) Assume infinity is a prime number.
(3) By definition of natural number, there exists a natural number X such that the successor of X is infinity. IOW, there exists some number that equals (infinity-1).
(4) Thus, infinity = S(S(S(S(...(1)...)))), where S is performed a finite number of times (by definition of natural number)
(5) Therefore, infinity is a finite number.
(6) Infinity is not a finite number, therefore we have a contradiction. Thus, infinity is not a prime number.
QED.