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New Possible Record Prime Number Found
An anonymous reader writes "The Great Internet Mersenne Prime Search (GIMPS), a distributed computing project, has probably found a new record prime number. Two verification runs have started; no errors were found in the initial calculation. The number of primes found lately, four in just over two years, is higher than previously expected. This prime is just under 10 million digits, which means that one of the participants in the project makes a good chance to obtain his or her part of the EFF prize of $100,000 for the first prime of over 10 million digits in the coming months. In 2000, one of the Gimps participants collected the $50,000 reward offered."
Bah, show me a new non-Mersenne prime and I'll be impressed...
To be honest. Why not? Sure a cure for cancer would be great, but for some, research for the sake of research is interesting. I am curious as to what Mersenne primes are calculable. Is that not sufficient justification?
When you're brute-forcing your way to a test for primality of n, you needn't go all the way to n / 2, only up to sqrt(n). If xy = n, and x > sqrt(n), then you should have found the factor y already.
I think there are also more efficient tests that can determine whether a number is prime to arbitrary probability without trying every possible divisor; not my field of expertise, though. Inquire of Google for isprime algorithms.
Real Daleks don't climb stairs - they level the building.
The Prime Number Theorem tells us that in a region of d around a large number n, there are approximately d/ln n primes. For a 9 million digit n, ln n is about 21 million, so one expects to see one prime every 21 million numbers. For example, between 10^9000000 and 1.1*10^9000000, one expects 5*10^8999991 prime numbers.
Because pure mathematics sometimes turns out to have unexpected real-world benefits. Ancient Greek mathematicians such as Apollonius of Perga studied properties of the conic sections (circles, ellipses, the parabola, the hyperbola) as pure maths with no expectation of practical gain. Two thousand years later, we found that planets move in ellipses, that projectiles follow parabolic paths, and so on. Hey presto, that ancient pure mathematics becomes useful...
I cannot speak for the EFF. But I do know several people directly involved with the administration of those awards, and have discussed many topics with them.
The smaller prizes - 1M digit (already awarded), and 10M digits (still pending) are actually pretty small and unimportant. They can be attacked simply by throwing huge numbers of inexpensive commodity PCs at the task. That's basically what GIMPS is. The larger prizes are the important ones, as they reward a much harder achievement. The algorithms used to tackle such tasks don't scale particularly well. It's more than 10 times harder to do a problem 10 times bigger. This in part is because of the hierarchical memory system that PCs have. Small fast caches, other medium-sized slower caches, and then large quantities of relatively slow main memory. FFTs really don't like such a hierarchical memory architecture, as they grab data from all over the place all of the time. Caches become very hard to use effectively, and enormous L1 caches are prohibitively expensive.
So these later prizes will almost certainly be awarded to systems either based on new algorithms that are vastly more scalable than current FFTs, or on new hardware (memory) designs which somehow get around the caching issue.
Moving up to even larger sizes, it may become impractical to perform such calculations on a single PC. Therefore communications systems will want to be invented that provide no more latency than main memory.
Those are real concrete advances in computer technology, and it's those that are being rewarded. The primes are almost a red herring.
Also FatPhil on SoylentNews, id 863
only 10 characters are used in the file, of course it will shrink by at least 50%
Mersenne prime finding is not the same as verifying a universal truth like 2*a = a+a. It is *NOT* yet proven that the number of Mersenne primes is infinite. So it is not a guarantee that you run a huge collection of machines and you always find the next bigger mersenne prime. The fact that we do indeed find them, makes it more convincing that the conjecture (that the number of mersenne primes is in fact infinite) is true.
> Jesus saved me from my past. He can save you as well.
Lectures on religion don't suddenly become any less tedious when presented by people stupid enough to get caught by the police. Please fuck off.