Seventeen or Bust
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 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. 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 so far by the project are:
|k||n||Digits of k2n+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 sequences:
- 10223×2n +1
- 19249×2n +1
- 21181×2n +1
- 22699×2n +1
- 24737×2n +1
- 33661×2n +1
- 55459×2n +1
- 67607×2n +1