Seventeen or Bust is a distributed computing project attempting to solve the Sierpinski problem. The name of the project is due to the fact that, when founded, there were seventeen values of k < 78,557 for which no primes were known.
The project was conceived in March of 2002 by two college undergraduates. After some planning and a lot of programming, the first public client was released on April 1. The project is now administered by:
 Louis Helm, a computer engineer in Austin, Texas.
 David Norris, a software engineer in Urbana, Illinois.
 Michael Garrison, a Computer Science undergraduate at Eastern Michigan University in Ypsilanti, Michigan.
As of January of 2010, Seventeen or Bust has eliminated eleven of those seventeen candidates. The project might now be styled "Six or Bust," but the original name will be kept for consistency.
Seventeen or Bust's eleven prime discoveries are:
 46157*2^698207+1 with 210,186 decimal digits, discovered November 27, 2002. Crunched by Stephen Gibson.
 65567*2^1013803+1 with 305,190 decimal digits, discovered December 2, 2002. Crunched by James Burt.
 44131*2^995972+1 with 299,823 decimal digits, discovered December 5, 2002. Crunched by an anonymous participant.
 69109*2^1157446+1 with 348,431 decimal digits, discovered December 6, 2002. Crunched by Sean DiMichele.
 54767*2^1337287+1 with 402,569 decimal digits, discovered December 23, 2002. Crunched by Peter Coels.
 5359*2^5054502+1 with 1,521,561 decimal digits, discovered December 6, 2003. Crunched by Randy Sundquist.
 28433*2^7830457+1 with 2,357,207 decimal digits, discovered December 30, 2004. Crunched by a member of Team Prime Rib.
 27653*2^9167433+1 with 2,759,677 decimal digits, discovered June 8, 2005. Crunched by Derek Gordon.
 4847*2^3321063+1 with 999,744 decimal digits, discovered October 15, 2005. Crunched by Richard Hassler.
 19249*2^13018586+1 with 3,918,990 decimal digits, discoverd March 26, 2007. Crunched by Konstantin Agafonov.
 33661*2^7031232+1 with 2,116,617 decimal digits, discovered October 17, 2007. Crunched by Sturle Sunde.
About the Sierpinski Problem
Wacław Franciszek Sierpiński (14 March 1882 — 21 October 1969), a Polish mathematician, was known for outstanding contributions to set theory, number theory, theory of functions and topology. It is in number theory where we find the Sierpinski problem.
Basically, the Sierpinski problem is "What is the smallest Sierpinski number"
First we look at Proth numbers (named after the French mathematician François Proth). A Proth number is a number of the form k*2^n+1 where k is odd, n is a positive integer, and 2^n>k.
A Sierpinski number is an odd k such that the Proth number k*2^n+1 is not prime for all n. For example, 3 is not a Sierpinski number because n=2 produces a prime number (3*2^2+1=13). In 1962, John Selfridge proved that 78,557 is a Sierpinski number...meaning he showed that for all n, 78557*2^n+1 was not prime.
Most number theorists believe that 78,557 is the smallest Sierpinski number, but it hasn't yet been proven. In order to prove it, it has to be shown that every single k less than 78,557 is not a Sierpinski number, and to do that, some n must be found that makes k*2^n+1 prime.
The smallest proven prime Sierpinski number is 271,129. In order to prove it, it has to be shown that every single prime k less than 271,129 is not a Sierpinski number, and to do that, some n must be found that makes k*2^n+1 prime.
Seventeen or Bust is working on the Sierpinski problem and the Prime Sierpinski Project is working on the prime Sierpinski problem. The following k's remain for each project:
 Sierpinski problem
 10223, 21181, 22699, 24737, 55459, 67607
 'prime' Sierpinski problem
 10223*, 22699*, 67607*, 79309, 79817, 90527, 152267, 156511, 168451, 222113, 225931, 237019,

 being tested by Seventeen or Bust
Fortunately, the two projects combined their sieving efforts into a single file. Therefore, PrimeGrid's PSP/SoB sieve supports both projects.
Additional Information
For more information about Sierpinski, Sierpinski number, and the Sierpinsk problem, please see these resources:
 Wacław Franciszek Sierpiński (WIKI)
 Sierpinski number / The Sierpinski problem (WIKI)
 The Sierpinski problem (Prothsearch)