Quote:
Originally Posted by MathDoggy
It is impossible because we constructed an arbitrary number Q which is the product of the finite list of the twin primes and adding 1 to the product

This is not a reason. You have constructed a number Q which is not divisible by your list of twin primes, and then you assume it must be divisible by a twin prime. You have no justification for the belief that Q must be divisible by a twin prime; in fact, you have constructed Q specifically such that it is NOT divisible by a twin prime, and then you claim a contradiction by just saying Q is divisible by a twin prime.
Your Q is divisible by 2 (do you see why?). All other claims about properties of Q's factors must be proven. Prove your claim.