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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 List of perfect numbers ： ウィキペディア英語版 List of perfect numbers The following is a list of the known perfect numbers, along with the Mersenne prime exponent ''p'' which generates them with the expression 2''p''−1× (2''p'' − 1) where 2''p'' − 1 is a Mersenne prime. All even perfect numbers are of this form. It is not known whether there are any odd perfect numbers. there are 48 known perfect numbers in total.〔(【引用サイトリンク】publisher=MIT )〕〔Chris Caldwell, "(Mersenne Primes: History, Theorems and Lists )" at The Prime Pages. Retrieved 2009-09-19.〕 The ratio ''p'' / digits approaches log(10) / log(4) = 1.6609640474... The displayed ranks are among those perfect numbers which are known as of November 2014. Some ranks may change later if smaller perfect numbers are discovered. It is known there is no odd perfect number below 101500.〔Ochem, Pascal; Rao, Michael, ("Odd Perfect Numbers Are Greater Than 10^1500" ), ''MATHEMATICS OF COMPUTATION'', Volume 81, Number 279, July 2012, Pages 1869–1877. S 0025-5718(2012)02563-4. Article electronically published on January 30, 2012〕 GIMPS reported that by 8 November 2014 the search for Mersenne primes (and thereby even perfect numbers) became exhaustive up to the 44th above.〔"("GIMPS Milestones Report" ). Retrieved 2014-11-16.〕 ==References== 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「List of perfect numbers」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.