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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. The project has solved eleven cases, and continues to search for solutions to the remaining six.〔(Seventeen or Bust: Project Stats )〕 ==Goals== The goal of the project is to prove that 78557 is the smallest Sierpinski number, that is, the least odd ''k'' such that ''k''·2''n''+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 was 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''·2''n''+1, … testing candidate values ''n'' using Proth's theorem. If one is found, that proves ''k'' is not a Sierpinski number. 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 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.〔(【引用サイトリンク】title=Sierpinski number )〕 Every known Sierpinski number ''k'' has a small ''covering set'', a finite set of primes with at least one dividing ''k''·2''n''+1 for each ''n''>0. For example, for the smallest known Sierpinski number, 78557, the covering set is The second generation of the client is based on Prime95, which is used in the Great Internet Mersenne Prime Search. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Seventeen or Bust」の詳細全文を読む スポンサード リンク
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