Ok, either the game wasn't fun enough or I killed it.

My pattern was any prime that was either one less or one more then a power of 2.

However, an interesting thought occurred this morning:

I was thinking about icons (you know, 32x32 pixels) and that one image that was sent out in to space as a sequence of bits Prime1XPrime2 long (so that there are only four 2d ways of decoding it, and it hints at that, and 2 of those ways are just reverses of each other, as if looking at it from the underside/behind. It only makes sense in one of those two classes of ways too.).

So I thought of 31, and then I wanted the next smallest prime, and thought 29. What's interesting to me, is that they are apart by exactly 2.

Then I started thinking, how could that be extended?

I realized that any -other- prime couldn't ever extend off of a prime, because it would always lead to a multiple of 2. Unless maybe it's a prime-prime extension, but I think that's going too far.

What if it were possible to describe prime numbers using only existing primes that are one off a base of 2, and bases of 2. I wonder if anyone's done research in to that... I don't think it'd be easy to google for (I could be wrong), but maybe someone else has run across it?

Either way, get me a link or make a search result for google that seems fitting, and I'll take that as a valid answer. (Then you provide the next pattern please.)