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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 Euclid–Mullin sequence ： ウィキペディア英語版 Euclid–Mullin sequence The Euclid–Mullin sequence is an infinite sequence of distinct prime numbers, in which each element is the least prime factor of one plus the product of all earlier elements. They are named after the ancient Greek mathematician Euclid, because their definition relies on an idea in Euclid's proof that there are infinitely many primes, and after Albert A. Mullin, who asked about the sequence in 1963.〔.〕 The first 51 elements of the sequence are :2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, 2801, 11, 17, 5471, 52662739, 23003, 30693651606209, 37, 1741, 1313797957, 887, 71, 7127, 109, 23, 97, 159227, 643679794963466223081509857, 103, 1079990819, 9539, 3143065813, 29, 3847, 89, 19, 577, 223, 139703, 457, 9649, 61, 4357, 87991098722552272708281251793312351581099392851768893748012603709343,〔(Factoring 43rd term of Euclid–Mullin sequence )〕〔http://escatter11.fullerton.edu/nfs/forum_thread.php?id=102&postid=398#398〕 107, 127, 3313, 227432689108589532754984915075774848386671439568260420754414940780761245893,〔(Factoring EM47 )〕 59, 31, 211... These are the only known elements . Finding the next one requires finding the least prime factor of a 335-digit number (which is known to be composite). ==Definition== If ''an'' denotes the ''n''-th element of the sequence, then ''an'' is the least prime factor of :$\backslash left(\backslash prod\_\; a\_i\backslash right)+1\backslash ,.$ The first element is therefore the least prime factor of the empty product plus one, which is 2. The element 13 in the sequence is the least prime factor of 2 × 3 × 7 × 43 + 1 = 1806 + 1 = 1807 = 13 × 139. 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「Euclid–Mullin sequence」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.