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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Proth number ： ウィキペディア英語版 Proth number In number theory, a Proth number, named after the mathematician François Proth, is a number of the form :$k\; \backslash cdot\; 2^n+1$ where $k$ is an odd positive integer and $n$ is a positive integer such that $2^n\; >\; k$. Without the latter condition, all odd integers greater than 1 would be Proth numbers. The first Proth numbers are : :3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, etc. The Cullen numbers (''n''·2''n''+1) and Fermat numbers (22''n''+1) are special cases of Proth numbers. == Proth primes == A Proth prime is a Proth number which is prime. The first Proth primes are (): :3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857. The primality of a Proth number can be tested with Proth's theorem which states that a Proth number $p$ is prime if and only if there exists an integer $a$ for which the following is true: :$a^\}\backslash equiv\; -1\backslash \; \backslash pmod$ The largest known Proth prime is $19249\; \backslash cdot\; 2^\; +\; 1$.〔Chris Caldwell, (The Top Twenty: Proth ), from The Prime Pages.〕 It was found by Konstantin Agafonov in the Seventeen or Bust distributed computing project which announced it 5 May 2007.〔(Press Release by Seventeen or Bust ). 5 May 2007.〕 It is also the largest known non-Mersenne prime.〔Chris Caldwell, (The Top Twenty: Largest Known Primes ), from The Prime Pages.〕 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「Proth number」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.