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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 Cunningham chain ： ウィキペディア英語版 Cunningham chain In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes. ==Definition== A Cunningham chain of the first kind of length ''n'' is a sequence of prime numbers (''p''1, ..., ''p''''n'') such that for all 1 ≤ ''i'' < ''n'', ''p''''i''+1 = 2''p''''i'' + 1. (Hence each term of such a chain except the last one is a Sophie Germain prime, and each term except the first is a safe prime). It follows that : $$ \begin p_2 & = 2p_1+1, \\ p_3 & = 4p_1+3, \\ p_4 & = 8p_1+7, \\ & -1). \end Or, by setting $a\; =\; \backslash frac$ (the number $a$ is not part of the sequence and need not be a prime number), we have $p\_i\; =\; 2^\; a\; -\; 1$ Similarly, a Cunningham chain of the second kind of length ''n'' is a sequence of prime numbers (''p''1,...,''p''''n'') such that for all 1 ≤ ''i'' < ''n'', ''p''''i''+1 = 2''p''''i'' − 1. It follows that the general term is : $p\_i\; =\; 2^p\_1\; -\; (2^-1)\; \backslash ,$ Now, by setting $a\; =\; \backslash frac$, we have $p\_i\; =\; 2^\; a\; +\; 1$. Cunningham chains are also sometimes generalized to sequences of prime numbers (''p''1, ..., ''p''''n'') such that for all 1 ≤ ''i'' ≤ ''n'', ''p''''i''+1 = ''ap''''i'' + ''b'' for fixed coprime integers ''a'', ''b''; the resulting chains are called generalized Cunningham chains. A Cunningham chain is called complete if it cannot be further extended, i.e., if the previous or next term in the chain would not be a prime number anymore. 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「Cunningham chain」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.