Seventeen or Bust
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Seventeen or Bust is a distributed computing project to solve the Sierpinski problem.
The goal of the project is to prove that 78,557 is the smallest Sierpinski number, that is the least k such that k·2n+1 is composite (i.e. not prime) for all n. Before the project began, there were only seventeen values of k < 78557 that had not been eliminated. The project is searching for values of n for which k·2n+1 is prime, thereby proving that k is not a Sierpinski number.
If the goal is reached, the conjecture of the Sierpinski problem will be proven true. So far prime numbers have been found in nine of the sequences, leaving eight for testing.
There is also the possibility that some of the remaining sequences contain no prime numbers; if that possibility weren't present, the problem would not be interesting. In that case, the search would continue forever, searching for prime numbers where none can be found. However, since no mathematician trying to prove that one of the remaining sequences contains only composite numbers has ever been successful, the conjecture is generally believed to be true.
The nine prime numbers found so far by the project are:
| k | n | Digits of k·2n+1 | Date of discovery |
|---|---|---|---|
| 4847 | 3321063 | 999744 | October 15, 2005 |
| 27653 | 9167433 | 2759677 | June 8, 2005 |
| 28433 | 7830457 | 2357207 | December 30, 2004 |
| 5359 | 5054502 | 1521561 | December 6, 2003 |
| 54767 | 1337287 | 402569 | December 22, 2002 |
| 69109 | 1157446 | 348431 | December 7, 2002 |
| 44131 | 995972 | 299823 | December 6, 2002 |
| 65567 | 1013803 | 305190 | December 3, 2002 |
| 46157 | 698207 | 210186 | November 27, 2002 |
Note that each of the these numbers has enough digits to fill up a middle-sized novel, at least. The project is presently dividing numbers among its active users, in hope of finding a prime number in the following eight sequences:
- (k·2n+1) for k=10223,19249,21181,22699,24737,33661,55459,67607.
