First off, a twin prime is a set of two consecutive odd numbers both of which are primes.
Most mathematicians believe that the twin prime series is an infinite one. The conjecture though, has never been proven.
I came up with a simple proof by method of contradiction.
Consider the twin prime series to be S
S = (3,5) , (11,13) , (17,19) , (29,31) ..... (N-1, N+1)
Where (N-1, N+1) is the last twin prime.
Take the product of all the primes till (N+1) to get a number, P.
P = 1 x 2 x 3 x 5 x 7 x 11 x .... x (N-1) x (N+1)
(P+1) will not be divisible by any prime number, making it a prime.
Similarly, (P-1) won't be divisible by any prime. Making it a prime as well.
Therefore, (P+1, P-1) is a twin prime.
And by contradiction, (N+1, N-1) is not the final twin prime.
Conclusively, the series is infinite.
Now, as I said the argument is very simple and it'd be ludicrous to think I'm the first to think of it. Which further means there is a hole or error in it somewhere. So, if you spot anything, help me out.