- Seventeen or Bust
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Seventeen or Bust is a distributed computing project started in March 2002 to solve the last seventeen cases in the Sierpinski problem.
Contents
Goals
Seventeen or Bust client
The goal of the project is to prove that 78557 is the smallest Sierpinski number, that is, the least odd k such that k·2n+1 is composite (i.e. not prime) for all n > 0. When the project began, there were only seventeen values of k < 78557 for which the corresponding sequence is not known to contain a prime.
For each of those seventeen values of k, the project is searching for a prime number in the sequence
- k·21+1, k·22+1, …, k·2n+1, …
using Proth's theorem, thereby proving that k is not a Sierpinski number. So far, the project has found prime numbers in eleven of the sequences, and is continuing to search in the remaining six. If the goal is reached, the conjectured answer 78557 to the Sierpinski problem will be proven true.
There is also the possibility that some of the remaining sequences contain no prime numbers. In that case, the search would continue forever, searching for prime numbers where none can be found. However, there is some empirical evidence suggesting the conjecture is true.[1]
Every known Sierpinski number k has a small covering set, a finite set of primes with at least one dividing k·2n+1 for each n>0. For example, for the smallest known Sierpinski number, 78557, the covering set is {3,5,7,13,19,37,73}. For another known Sierpinski number, 271129, the covering set is {3,5,7,13,17,241}. None of the remaining sequences has a small covering set (that can be easily tested) so it is suspected that each of them contains primes.
The second generation of the client is based on Prime95, which is used in the Great Internet Mersenne Prime Search.
Prime number discoveries
The Seventeen or Bust set, with data for the eleven prime numbers eliminated to date:[2]
# k n Digits of k·2n+1 Date of discovery Found by 1 4,847 3,321,063 999,744 15 Oct 2005 Richard Hassler 2 5,359 5,054,502 1,521,561 06 Dec 2003 Randy Sundquist 3 10,223 > 17,000,000 (Search in progress) 4 19,249 13,018,586 3,918,990 26 Mar 2007 Konstantin Agafonov 5 21,181 > 17,000,000 (Search in progress) 6 22,699 > 17,000,000 (Search in progress) 7 24,737 > 15,900,000 (Search in progress) 8 27,653 9,167,433 2,759,677 08 Jun 2005 Derek Gordon 9 28,433 7,830,457 2,357,207 30 Dec 2004 Anonymous 10 33,661 7,031,232 2,116,617 13 Oct 2007 Sturle Sunde 11 44,131 995,972 299,823 06 Dec 2002 deviced (nickname) 12 46,157 698,207 210,186 26 Nov 2002 Stephen Gibson 13 54,767 1,337,287 402,569 22 Dec 2002 Peter Coels 14 55,459 > 17,000,000 (Search in progress) 15 65,567 1,013,803 305,190 03 Dec 2002 James Burt 16 67,607 > 17,000,000 (Search in progress) 17 69,109 1,157,446 348,431 07 Dec 2002 Sean DiMichele As of August 2009[update] the largest of these primes, 19249·213018586+1, is the largest known prime that is not a Mersenne prime.[3]
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 each of the six remaining sequences:
- k·2n+1, for k = 10223, 21181, 22699, 24737, 55459, 67607.
See also
- Riesel Sieve, a related distributed computing project for numbers of the form k·2n−1
- List of distributed computing projects
- PrimeGrid - biggest search for primes.
- Computer-assisted proof
References
External links
Categories:- Distributed computing projects
- Analytic number theory
- 2002 establishments
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