Looks at crowd of emasculated married men...

Because negative integers aren't prime. A prime number is defined as "a number larger than 1 that cannot be expressed as a product of natural numbers that are all smaller than it."

Since negative integers aren't larger than 1, they can't be prime by definition.

Here's another proof I came up with, in which I prove that i (the square root of -1) is a real number.

Suppose x is real. Then x is either 0 or not 0. If x is 0, sqrt(x) is clearly 0, which is a real number.

Now, if x != 0, then either x > 0 or x < 0. Without loss of generality, take x > 0 (in other words, x is positive). Since x is positive, it has 2 square roots, both real.

Hence, since x is either 0 or not 0, x must clearly have a real square root.

Now that we've established that every real x has at least one real square root, we let x = -1; hence, we conclude that -1 must have a real square root. Hence, i, the square root of -1, must be real.
QED.

I know that feel. I'm good at mathematics, but I still have a latent terror of it. I have no idea why I chose to do physics.

The assumption is A=B. A-B=0.

B(A-B) = (A+B) (A-B) Cancel out the like elements

Division by 0.

Well, that statement *is* true modulo 11 (or modulo any factor of 11, not that you have much choice in the matter here).\

Here's another one:
To fairly divide a pizza between 2 people, one person cuts the pizza, and the other one chooses a side to take.
To fairly divide a pizza between 1 person, that person "cuts" the pizza, and then chooses one out of the one pizzas.
How do you fairly divide a pizza between 0 people?

(By the way, dividing a pizza between 3 or more pizzas can't be done this easily, particularly if you adopt the (reasonable) rule that any person't portion of the pizza must be in a single slice, and no part of the pizza can go unclaimed.)

uhhhhhhh, no. :P

Late to the party but: The sequence 2, 4, 6, 10, 14, 22, 26, 34, 38, ... (OEIS A001747) consisting of the number 2 together with the primes multiplied by 2 is sometimes also called the even primes, since these are the even numbers n=2k that are divisible by just 1, 2, k, and 2k. From here.
Anyway proof is really simple. Let's say we have 2 "even primes", p = 2k, q = 2l. So naturally q - p = 2l - 2k, resulting q - p = 2 (l -k) thus m-n is even.