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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 Firoozbakht's conjecture ： ウィキペディア英語版 Firoozbakht's conjecture In number theory, Firoozbakht’s conjecture (or the Firoozbakht conjecture) is a conjecture about the distribution of prime numbers. It is named after the Iranian mathematician Farideh Firoozbakht from the University of Isfahan who stated it first in 1982. The conjecture states that $p\_^$ (where $p\_n$ is the ''n''th prime) is a strictly decreasing function of ''n'', i.e., : Equivalently: see , . By using a table of maximal gaps, Farideh Firoozbakht verified her conjecture up to 4.444.〔 Now with more extensive tables of maximal gaps, the conjecture has been verified for all primes below 4.〔(Gaps between consecutive primes )〕 If the conjecture is true, then the prime gap function $g\_n\; =\; p\_\; -\; p\_n$ satisfies 〔.〕 This is one of the strongest upper bound ever conjectured for prime gaps, even somewhat stronger than ''Cramer-Shanks conjecture''.〔(【引用サイトリンク】first=Alexei )〕 It implies a strong form of Cramér's conjecture but is inconsistent with the heuristics of Granville and Pintz〔.〕〔.〕 which suggest that $g\_n\; >\; \backslash frac(\backslash log\; p\_n)^2$ infinitely often for any $\backslash varepsilon>0,$ where $\backslash gamma$ denotes Euler's constant. Both are consistent with Daniel Shanks' conjectured asymptotic equality of record gaps.〔.〕 Two related conjectures (see the comments of ) are :, which is weaker. And, : for all values with $n\; >\; 5$, which is stronger. ==See also== *Prime number theorem *Andrica's conjecture *Legendre's conjecture *Oppermann's conjecture 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「Firoozbakht's 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.