Seventeen or Bust
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How they are attacking the problem
The aim of the project is to find primes of the form [math]k*2^n+1[/math], where k is one of the remaining 17 (now 5) candidates for Sierpiński numbers smaller than 78557, and n a positive integer. In order to find such a prime, we have a long queue of candidates, and we are running primality tests called PRP (PRobable Prime), which take a very long time, for every candidate in the queue.
Because PRP takes so much computational power, we try to eliminate as many non-prime numbers as possible from the queue by sieving, which means to take a (relatively) small integer and check whether it is a factor of one of the tests we are going to run. If there is a factor, the number is not prime and thus doesn't need to be tested.
Finally, before running a particular test, one can make a last effort to find a factor for the particular k,n-pair in a few hours before running a test which will take several weeks, by p-1 factoring.
As of April 2010, Seventeen Or Bust has discovered eleven huge prime numbers. The four largest discoveries ranks as the tenth to thirteenth largest prime ever discovered, and they are the largest prime that are not a Mersenne prime. Six of the eleven primes rest in the Top 100.
The project was originally a collaboration between long-time friends Louie Helm and David Norris. The first public version of the software was released on 2002-04-01. Since then, many people have contributed in various ways to the project. MikeGarrison is our system administrator and does a great job taking care of the machines our server runs on. Phil Chapman, Fritz Redeker and Matt Edson have donated a lot of hardware and currently provide for our Internet hosting. George Woltman contributed the hand-tuned assembly code that makes our software so fast. Many others have contributed mathematical, logistical and practical insight, suggestions, and moral support.