A bit less than perfect

Fact:

For all numbers $z$, $z^{2}-1=(z+1)\times(z-1)$

Five math students are discussing this subject:

Alice: "Since $z^{2}-1$ is a product of 2 numbers, all positive integers 1 less than a perfect square are composite."

Ben: "All integers 1 more than a perfect square are prime."

Charlie: "The lowest possible value for $z^{2}-1$, where $z$ is any number, is $-1$."

Drake: "None of you are correct."

Emily: "To build off of what Drake said, all of you are wrong because the equation itself is wrong."

Which student is correct?

For clarity: When the term, "number," is stated, it means any number that can be found in the complex plane.