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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 Gillies' conjecture ： ウィキペディア英語版 Gillies' conjecture In number theory, Gillies' conjecture is a conjecture about the distribution of prime divisors of Mersenne numbers and was made by Donald B. Gillies in a 1964 paper in which he also announced the discovery of three new Mersenne primes. The conjecture is a specialization of the prime number theorem and is a refinement of conjectures due to I. J. Good and Daniel Shanks. The conjecture remains an open problem, although several papers have added empirical support to its validity. ==The conjecture== :$\backslash text$ :$\backslash text(B)\backslash text$ ::$$ \text\sim \begin \log(\log B /\log A) & \textA \ge 2p\\ \log(\log B/\log 2p) & \text A < 2p \end He noted that his conjecture would imply that # The number of Mersenne primes less than $x$ is $~\backslash frac\; \backslash log\backslash log\; x$. # The expected number of Mersenne primes $M\_p$ with $x\; \backslash le\; p\; \backslash le\; 2x$ is $\backslash sim2$. # The probability that $M\_p$ is prime is $~\backslash frac$. 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「Gillies' conjecture」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.