Friday, December 26, 2008

Twin Primes

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.

Sunday, December 14, 2008

Guten tag

I just created this blog for two reasons. First off, I fancied the name. And secondly, I wanted to try out a new blogger template which I wasn't willing to use on my other existing blog because then I inexorably lose all my gadgets.
I had two options for the template. The alternative had eldritch green fumes along the periphery. But I settled for this one since it reminds me of ńĆerenkov radiations. And the reason for the pop-up comment box is that blogger decided to bug the regular one.
Ah, and concerning the title of this post, I've always wanted to learn German among a dozen other languages. Maybe I'll get to that sometime.

So, here I welcome you to my new blog which I will hopefully be inspired to use sometime.