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111 (One hundred () eleven) is the natural number following 110 and preceding 112. ==In mathematics== 111 is a perfect totient number. 111 is R3 or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like 222 or 777) in base ten are of the form 3''n'' × 37. As a repunit, it also follows that 111 is a palindromic number. All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. 111 is not prime in base ten, but is prime in base two, where 1112 = 710. It is also prime in these other bases up to 128: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, 99, 101, 105, 110, 111, 117, 119 In base 18, the number 111 is 73 (= 34310) which is the only base where 111 is a perfect power. The smallest magic square using only 1 and prime numbers has a magic constant of 111: A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111: (The square has this magic constant because 1 + 2 + 3 + ... + 34 + 35 + 36 = 666, and 666 / 6 = 111). 111 is also the magic constant of the n-Queens Problem for n = 6. It is also an nonagonal number. In base 10, it is a Harshad number. ==Nelson== (詳細はAdmiral Nelson, who allegedly only had "One Eye, One Arm, One Leg" near the end of his life. This is in fact inaccurate - Nelson never lost a leg. Alternate meanings include "One Eye, One Arm, One Ambition" and "One Eye, One Arm, One Arsehole". It is particularly known as a score in cricket. A score of 111 or multiples thereof (222 = "double nelson", 333 = "triple nelson" and so on) is considered unlucky by some in English cricket: most famously by the international umpire David Shepherd, who had a whole retinue of peculiar mannerisms - hops, shuffles, jiggles and so on - that he would indulge in if the score was ever a "Nelson" multiple. Particularly if the number of wickets also matched - 111/1, 222/2 etc. 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「111 (number)」の詳細全文を読む スポンサード リンク
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