Finding the First Trillion Congruent Numbers 94
eldavojohn writes "First stated by al-Karaji about a thousand years ago, the congruent number problem is simplified to finding positive whole numbers that are the area of a right triangle with rational number sides. Today, discovering these congruent numbers is limited only by the size of a computer's hard drive. An international team of mathematicians recently decided to push the limits on finding congruent numbers and came up with the first trillion. Their two approaches are outlined in detail, with pseudo-code, in their paper (PDF) as well as details on their hardware. For those of you familiar with this sort of work, the article provides links to solving this problem — from multiplying very large numbers to identifying square-free congruent numbers."
Re:Why? (Score:4, Interesting)
According to TFA (I know, I know, we aren't supposed to do that, but I only skimmed it! I swear!!), this isn't particularly useful in itself, but the new techniques they had to develop to solve it are important. Specifically, they had to figure out news ways of multiplying numbers, since the numbers they wanted to multiply were larger than their hardware's main memory (OK, OK, a number that's trillions of bits long seems a bit far fetched to me too, but that's what TFA said.)
Hard Drive? (Score:3, Interesting)
Today the limitations of discovering these congruent numbers is limited only by the size of a computer's hard drive.
Can someone explain why they didn't use more than 2.7TB of HDD space if HDD space is the limiting factor?
Re:Why? (Score:1, Interesting)
Statistical analysis of the prime numbers gave us the insight needed to find a formula describing an upper bound for their frequency.
Sometimes in order to make an important realization, you have to work through near-pointless crap for a long time, hoping it will pay off.
Re:Why? (Score:3, Interesting)
"I'm so not a maths geek, but why is this useful other than being able to say 'hey, we found the first trillion congruent numbers'?"
I came here expecting to see this question, and was not disappointed.
The answer is: "For the same reason that people do crack."
Seriously. www.angrymath.com
Re:Hard Drive? (Score:2, Interesting)
I own the 128GB RAM, etc., computer that the second group did the computation on. I have a Sun X4550 24TB disk array (ZFS) connected to it, but I only allocated a few terabytes of space for a scratch disk. They were well into the calculation when I found out what they were up to (I was initially annoyed, since they were saturating the network). I think they were just being polite to me and the other users by not using a lot more disk.