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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 Cuban prime ： ウィキペディア英語版 Cuban prime A cuban prime is a prime number that is a solution to one of two different specific equations involving third powers of ''x'' and ''y''. The first of these equations is: :$p\; =\; \backslash frac,\backslash \; x\; =\; y\; +\; 1,\backslash \; y>0$〔Cunningham, On quasi-Mersennian numbers〕 and the first few cuban primes from this equation are : 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227 The general cuban prime of this kind can be rewritten as $\backslash tfrac$, which simplifies to $3y^2\; +\; 3y\; +\; 1$. This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal. the largest known has 65537 digits with $y\; =\; 100000845^$,〔Caldwell, Prime Pages〕 found by Jens Kruse Andersen. The second of these equations is: :$p\; =\; \backslash frac,\backslash \; x\; =\; y\; +\; 2,\backslash \; y>0.$〔Cunningham, Binomial Factorisations, Vol. 1, pp. 245-259〕 This simplifies to $3y^2\; +\; 6y\; +\; 4$. With a substitution $y\; =\; n\; -\; 1$ it can also be written as $3n^2\; +\; 1,\; \backslash \; n>1$. The first few cuban primes of this form are : :13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313 The name "cuban prime" has to do with the role cubes (third powers) play in the equations, and has nothing to do with Cuba. == See also == *Cubic function *List of prime numbers 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「Cuban prime」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.