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Seventeen or Bust

Seventeen Or Bust
General :
Purpose : To help solve the Sierpiński problem
Category : Primality test
Hardware / Software :
Platform : WIN, OSX, Unix, OpenBSD
Worktype : Sieving, LLR
Software : SB client
Website : Homepage
Status : defunct, absorbed into PrimeGrid
Started : 03-2002
Result : 11 k's eliminated as a standalone project, 1 k eliminated as a subproject on PrimeGrid
% completed : running
Ended : 04-2016 as a standalone project, not ended yet as a subproject on PrimeGrid

To rewrite: objective view, links update

Seventeen Or Bust (SOB) was a distributed computing project working on a problem in number theory called the Sierpiński problem. It is currently a subproject on PrimeGrid.

How they are attacking the problem

The aim of the project is to find primes of the form $\displaystyle{ k*2^n+1 }$, 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.

Results

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.

Credits

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.