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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 Hilbert number ： ウィキペディア英語版 Hilbert number |Gelfond–Schneider constant}} In number theory, a Hilbert number is defined as a positive integer of the form 4''n'' + 1 (). The Hilbert numbers were named after David Hilbert. The integer sequence of Hilbert numbers is 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, ... . A Hilbert prime is a Hilbert number that is not divisible by a smaller Hilbert number (other than 1). The sequence of Hilbert primes is 5, 9, 13, 17, 21, 29, 33, 37, 41, 49, 53, 57, 61, 69, 73, 77, 89, 93, 97, 101, 109, 113, 121, 129, 133, 137, 141, 149, 157, 161, 173, 177, 181, 193, 197, ... . Note that Hilbert primes do not have to be prime numbers; for example, 21 is a composite Hilbert prime. It follows from multiplication modulo 4 that a Hilbert prime is either a prime number of form 4''n'' + 1 (called a Pythagorean prime), or a semiprime of form (4''a'' + 3) × (4''b'' + 3). ==Hilbert factorization== 1 = unit 5 = prime 9 = prime 13 = prime 17 = prime 21 = prime 25 = 52 29 = prime 33 = prime 37 = prime 41 = prime 45 = 5 * 9 49 = prime 53 = prime 57 = prime 61 = prime 65 = 5 * 13 69 = prime 73 = prime 77 = prime 81 = 92 85 = 5 * 17 89 = prime 93 = prime 97 = prime 101 = prime 105 = 5 * 21 109 = prime 113 = prime 117 = 9 * 13 121 = prime 125 = 53 129 = prime 133 = prime 137 = prime 141 = prime 145 = 5 * 29 149 = prime 153 = 9 * 17 157 = prime 161 = prime 165 = 5 * 33 169 = 132 173 = prime 177 = prime 181 = prime 185 = 5 * 37 189 = 9 * 21 193 = prime 197 = prime 201 = prime 205 = 5 * 41 209 = prime 213 = prime 217 = prime 221 = 13 * 17 225 = 9 * 25 229 = prime 233 = prime 237 = prime 241 = prime 245 = 5 * 49 249 = prime 253 = prime 257 = prime 261 = 9 * 29 265 = 5 * 53 269 = prime 273 = 13 * 21 277 = prime 281 = prime 285 = 5 * 57 289 = 172 293 = prime 297 = 9 * 33 ... 441 = 9 * 49 = 212 (the first number that has more than one Hilbert factorizations) ... 693 = 9 * 77 = 21 * 33 ... 1089 = 9 * 121 = 332 ... 1197 = 9 * 133 = 21 * 57 ... 1617 = 21 * 77 = 33 * 49 ... Number with more than one Hilbert Factorizations are :441, 693, 1089, 1197, 1449, 1617, 1881, 1953, 2205, 2277, 2541, 2709, 2793, 2961, 3069, 3249, 3381, 3465, 3717, 3933, 3969, 4221, 4257, 4389, 4473, 4557, 4653, 4761, 4977, ... 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「Hilbert 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.