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Wednesday, September 12, 2012

ABC @ Home

I came across this story about prime numbers on Graham Hancock's website. Seems some dude has proven some conjecture about ABC Triples, whatever they are. The proof is only 500 pages long. I'm gonna sit down and read that just as soon as I win the lottery. The story doesn't do a good job of telling what an ABC Triple is, much less why we should care, so I fed it to Google and found some interesting stuff. The least interesting was this page that does a pretty good job of explaining what an ABC Triple is, and makes a pass at explaining why we might care.

A page on slashdot has an apparently endless discussion about how math articles in Wikipedia are only good for grad students, even the Wikipedia articles on algebra are of no help to any lesser beings, like a high school student who is trying to learn algebra.

I followed a link on another page and found that there are a whole bunch of these "@ home" projects going on. The idea behind "@ home" is there are some projects that might produce some useful results, if only enough computer power was available, so someone designs a program that can be run on a whole bunch of PC's independently, and encourages PC owners to download and run these programs. The programs run in the background and only when nothing else is going on, which for most computers is most of the time. So we are putting all those idle CPU cycles to use. I had heard that SETI was using this and there is a protein folding program floating around somewhere. There was even a program that was attempting to solve the Eternity II puzzle. This guy was running over a dozen. I don't even know what most of them are.

The picture comes from the original story. I thought it was an interesting take on prime numbers. Notice how most of the prime numbers line up on diagonals, or occupy corners. I wrote a simple prime number sieve some time ago and this prompted me to go look for it, but it seems to have vanished. No big loss, the prime number business has become a quagmire. I don't know how far they have gotten, but I imagine they are up into the hundreds of digits. With numbers up to a value of a million or so, it's kind of interesting, but once you've got a thousand prime numbers it's no longer fun. It's more like work.

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