[abuzzooz]

> It would seem to me that once you reach a certain threshold you won't be able to find two primes "close" to each other anymore because primes will be so far apart from each other. ]

That is not quite correct. The average gap between primes gets larger as you move further along the number line. But, you will still get the occasional consecutive odd numbers that are close to one another. In fact, there is an old conjecture (Twin Prime Conjecture[1]) that claims that there are an infinite number of pairs of consecutive primes separated by 2.

PS. I'm not a mathematician (engineer with some decent math background), so I might very well be wrong.

[1] http://en.wikipedia.org/wiki/Twin_prime

[fragsworth]

Yeah, this result is effectively getting a little bit closer to proving the Twin Prime Conjecture.

It would be interesting to see the proof get progressively closer to 2, but more and more difficult each time.