Seventeen or Bust Nixes Three Sierpinski Candidates

Craigj0 writes "In just 8 days Seventeen or bust has removed three Sierpinski candidates after people have been trying for years. Seventeen or bust is a distributed attack on the Sierpinski problem. You can find the first two press releases here(1) and here(2), the third is still to come. More information about Sierpinski numbers can be found here. Finally they could always use some more people so join!"

Speaking of Sierpinski...

[jonnyfish]

Way back when I was first learning DirectDraw (shudder), I wrote a program to generate pixel colors based on x, y, and time (ticks) values. I played with trig functions a little bit, trying to generate some plasma effects. Eventually I got bored of that and tried some operations using the bitwise operators and, amazingly, I got it to generate the Sierpinski triangle using something like 2 or 3 bitwise ands per pixel. I say amazingly because all I know about Sierpinski triangles is the name, so I generated it completely by accident. Needless to say, I was very surprised the first time I saw it.

How to prove this?

[Scarblac]

I've read around a bit now, I've even installed their client (wasn't currently doing any other distributed stuff, so why not), but I still don't understand the math well. I understand you can prove a number k is not a Sierpinski number by finding an n so that k*2^n+1 is prime. The lowest known Sierpinski number is 78557. There are now only 14 lower numbers left for which there's no fitting n found yet, and they're searching for them.

Now what I don't understand is how Sierpinski-ness can be proven, how they know there's not some huge n that makes 78557*2^n+1 prime after all; and I can't find the info. There's a class of numbers that are Sierpinski by construction (apparently) but they are much higher than this one. I guess there's no quick easy answer, I just have to read the literature, and I'm not going to... There are too many contrived number properties out there, and too much other stuff to do :)