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EspañolSEVENTEEN OR BUST
'Seventeen or Bust' is a distributed computing project to solve the last seventeen cases in the Sierpinski problem.
The goal of the project is to prove that 78,557 is the smallest Sierpinski number, that is, the least odd ''k'' such that ''k''·2''n''+1 is composite for all ''n'' > 0 (i.e. not prime for any ''n'').
When the project began, there were only seventeen values of ''k'' < 78,557 that were still in question.
For each of those seventeen values of ''k'', the project is searching for a value of ''n'' for which ''k''·2''n''+1 is prime, thereby proving that ''k'' is not a Sierpinski number.
So far, the project has found prime numbers in ten of the sequences, and is continuing to search the remaining seven.
If the goal is reached, the conjecture of the Sierpinski problem will be proven true.
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 ten prime numbers found so far by the project are:
As of August 2007 the largest of these primes, 19249·213018586+1, is the largest known prime that is not a Mersenne prime.[1]
Note that each of these numbers has enough digits to fill up a medium-sized novel, at least. The project is presently dividing numbers among its active users, in hope of finding a prime number in the seven remaining sequences:
:''k''·2''n''+1, for ''k'' = 10223, 21181, 22699, 24737, 33661, 55459, 67607.
★ Riesel Sieve, a related distributed computing project for numbers of the form ''k''·2''n''−1
★ List of distributed computing projects
★ Seventeen or Bust homepage
The goal of the project is to prove that 78,557 is the smallest Sierpinski number, that is, the least odd ''k'' such that ''k''·2''n''+1 is composite for all ''n'' > 0 (i.e. not prime for any ''n'').
When the project began, there were only seventeen values of ''k'' < 78,557 that were still in question.
For each of those seventeen values of ''k'', the project is searching for a value of ''n'' for which ''k''·2''n''+1 is prime, thereby proving that ''k'' is not a Sierpinski number.
So far, the project has found prime numbers in ten of the sequences, and is continuing to search the remaining seven.
If the goal is reached, the conjecture of the Sierpinski problem will be proven true.
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 ten prime numbers found so far by the project are:
| ''k'' | ''n'' | Digits of ''k''·2''n''+1 | Date of discovery |
|---|---|---|---|
| 19,249 | 13,018,586 | 3,918,990 | March 26, 2007 |
| 4,847 | 3,321,063 | 999,744 | October 15, 2005 |
| 27,653 | 9,167,433 | 2,759,677 | June 8, 2005 |
| 28,433 | 7,830,457 | 2,357,207 | December 30, 2004 |
| 5,359 | 5,054,502 | 1,521,561 | December 6, 2003 |
| 54,767 | 1,337,287 | 402,569 | December 22, 2002 |
| 69,109 | 1,157,446 | 348,431 | December 7, 2002 |
| 44,131 | 995,972 | 299,823 | December 6, 2002 |
| 65,567 | 1,013,803 | 305,190 | December 3, 2002 |
| 46,157 | 698,207 | 210,186 | November 27, 2002 |
As of August 2007 the largest of these primes, 19249·213018586+1, is the largest known prime that is not a Mersenne prime.[1]
Note that each of these numbers has enough digits to fill up a medium-sized novel, at least. The project is presently dividing numbers among its active users, in hope of finding a prime number in the seven remaining sequences:
:''k''·2''n''+1, for ''k'' = 10223, 21181, 22699, 24737, 33661, 55459, 67607.
| Contents |
| See also |
| External links |
See also
★ Riesel Sieve, a related distributed computing project for numbers of the form ''k''·2''n''−1
★ List of distributed computing projects
External links
★ Seventeen or Bust homepage
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