Clearly Q is larger than any other twin prime, so it does not equal one of them, since P1,P2,P3,P4...Pn constitute all twin primes Q can not be a twin prime. Thus it most be divisible by at least one of our finitely many twin primes, say Pk ( 1 less than or equal to k less than or equal to n) But when we divide Q by Pk we have a remainder of 1. This is a contradiction so our original assumption that there are finitely many twin prime must be false.
