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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 61 (number) ： ウィキペディア英語版 61 (number) 61 (sixty-one) is the natural number following 60 and preceding 62. ==In mathematics== It is the 18th prime number. The previous is 59, with which it comprises a twin prime. Sixty-one is a cuban prime of the form $p\; =\; (x^3\; -\; y^3)\; /\; (x\; -\; y),\; x\; =\; y\; +\; 1$. Sixty-one is the smallest ''proper prime'', a prime ''p'' which ends in the digit 1in base 10 and whose reciprocal in base 10 has a repeating sequence with length ''p''-1. In such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, (''p''-1)/10 times).〔Dickson, L. E., ''History of the Theory of Numbers'', Volume 1, Chelsea Publishing Co., 1952.〕 61 is 9th Mersenne prime exponent. (261 − 1 = ) Sixty-one is the sum of two squares, 52 + 62, and it is also a centered square number, a centered hexagonal number and a centered decagonal number. It is the sixth Euler zigzag number (or Up/down number). In base 14, 61 is a unique prime since no other prime has a 6-digit period in base 14. Since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8, 61 is a Pillai prime. In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131). It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61... 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「61 (number)」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.