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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 Andrica's conjecture ： ウィキペディア英語版 Andrica's conjecture Andrica's conjecture (named after Dorin Andrica) is a conjecture regarding the gaps between prime numbers. The conjecture states that the inequality : holds for all $n$, where $p\_n$ is the ''n''th prime number. If $g\_n\; =\; p\_\; -\; p\_n$ denotes the nth prime gap, then Andrica's conjecture can also be rewritten as : == Empirical evidence == Imran Ghory has used data on the largest prime gaps to confirm the conjecture for $n$ up to 1.3002 x 1016.〔''Prime Numbers: The Most Mysterious Figures in Math'', John Wiley & Sons, Inc., 2005, p.13.〕 Using a table of maximal gaps and the above gap inequality, the confirmation value can be extended exhaustively to 4 x 1018. The discrete function $A\_n\; =\; \backslash sqrt$ is plotted in the figures opposite. The high-water marks for $A\_n$ occur for n = 1, 2, and 4, with ''A''4 ≈ 0.670873..., with no larger value among the first 105 primes. Since the Andrica function decreases asymptotically as ''n'' increases, a prime gap of ever increasing size is needed to make the difference large as ''n'' becomes large. It therefore seems highly likely the conjecture is true, although this has not yet been proven. 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「Andrica'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.