Find the Problem with this Proof

My task is to find the flaw with the following given proof:

This "proof" attempts to prove that there do not exist any primes that are greater than 101.

Proof:

Let n > 101. Then it is evident if n is even, it's definitely not a prime.

If n is odd, then (n + 1)/2 and (n - 1)/2 are integers. Let x = (n + 1)/2 and y = (n - 1)/2. Then, n = x^2 - y^2 = (x + y)*(x-y), thus odd n is not a prime.

And thus the proof is complete proving that there do not exist any primes > 101.

Q.E.D?