Seventeen or bust

"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. To do so, all odd numbers less than 78,557 must be eliminated as possible Sierpinski numbers. If a number k2ⁿ + 1 is found to be prime, then k is proven not to be a Sierpinski number. Before the project began, all but seventeen numbers below 78,557 had been eliminated.

If the goal is reached, the conjecture of the Sierpinski problem will be proven true. So far prime numbers have been found in six of the sequences, leaving eleven 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. If there is such a sequence, the project would go on for eternity, searching for prime numbers where none can be found. However, since no mathematician trying to prove the remaining sequences contain only composite numbers has ever been successful, the conjecture is generally believed to be true.

The prime numbers found by the project are:

5359×2^5054502 + 1; 1,521,561 digits - discovered December 6, 2003

44131×2⁹⁹⁵⁹⁷² + 1; 299,823 digits - discovered December 6, 2002

46157×2⁶⁹⁸²⁰⁷ + 1; 210,186 digits - discovered 27 November, 2002

54767×2^1337287 + 1; 402,569 digits - discovered 22 December, 2002

65567×2^1013803 + 1; 305,190 digits - discovered 3 December, 2002

69109×2^1157446 + 1; 348,431 digits - discovered 7 December, 2002

Note that each of the last five numbers has enough digits to fill up a middle-sized novel.

The project is presently dividing numbers among its active users, in hope of finding a prime number in the following sequences:

4847×2ⁿ +1

10223×2ⁿ +1

19249×2ⁿ +1

21181×2ⁿ +1

22699×2ⁿ +1

24737×2ⁿ +1

27653×2ⁿ +1

28433×2ⁿ +1

33661×2ⁿ +1

55459×2ⁿ +1

67607×2ⁿ +1