Seventeen or Bust

Seventeen or Bust is a distributed computing project to prove the Sierpinski Conjecture. It has a website at http://www.seventeenorbust.com.

When the project started, there were 17 candidate Sierpinski numbers left to challenge the conjecture; the project sets out to find a number n for each of these k values so that k^.2ⁿ+1 is prime. If primes are found for all seventeen candidates, the theorem will be proven; if the conjecture is actually wrong, the search will go on forever, hence the name 'Seventeen or Bust'.

So far, five candidates have been eliminated by SoB, until 4 Jan 2003:

• 44131^.2⁹⁹⁵⁹⁷²+1 is prime
• 46157^.2⁶⁹⁸²⁰⁷+1 is prime
• 54767^.2^1337287+1 is prime
• 65567^.2^1013803+1 is prime
• 69109^.2^1157446+1 is prime

Update December 20, the sixth has been found:
5359^.2^5054502+1 is prime.

Proving that a number of this form is prime is relatively easy because of Proth's Theorem, but with numbers this big (the 54767 one has 402569 digits!) it still takes a long time.

To make it faster, many many possible n values are first eliminated for each k by the SoB team, using an algorithm known as Eratosthenes' Sieve. By making sure candidate numbers have no "small" factors (say, none below 2,000,000,000), their number is greatly reduced.

The remaining numbers are sent to Internet users participating in the project, a cast of thousands. They can test each number using Proth's Theorem, a process that takes hours or days depending on the speed of the computer.

It's expected to take a few more years to finish.

Their client is based on the math libraries of GIMPS founder George Woltman. Also, it is very likely that the project will never succeed - quite frankly, it is likely that some of the numbers to be eliminated will need to be tested further than present hardware can test in less than several months.

Also, they actually sieve far, far higher than 2,000,000,000. The reason is that it's possible to use special software like NewPGen to sieve an entire range of numbers at once. In particular, for the form k.2ⁿ+1 described above, a candidate factor can be compared to all the candidate prime numbers with a given k at once. This means that it makes sense to sieve into the trillions or quadrillions, since you'll still be factoring away a significant number of candidates. Google on "NewPGen" for more info.