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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 Cousin prime ： ウィキペディア英語版 Cousin prime In mathematics, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences and in OEIS) below 1000 are: :(3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 443), (457, 461), (463,467), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971) == Properties == The only prime belonging to two pairs of cousin primes is 7. One of the numbers ''n'', ''n''+4, ''n''+8 will always be divisible by 3, so ''n'' = 3 is the only case where all three are primes. the largest known cousin prime was (''p'', ''p'' + 4) for :''p'' = (311778476 · 587502 · 9001# · (587502 · 9001# + 1) + 210)·(587502 · 9001# − 1)/35 + 1 where 9001# is a primorial. It was found by Ken Davis and has 11594 digits. The largest known cousin probable prime is :474435381 · 298394 − 1 :474435381 · 298394 − 5. It has 29629 digits and was found by Angel, Jobling and Augustin.〔(474435381 · 298394 − 1 ). Prime pages.〕 While the first of these numbers has been proven prime, there is no known primality test to easily determine whether the second number is prime. It follows from the first Hardy–Littlewood conjecture that cousin primes have the same asymptotic density as twin primes. An analogue of Brun's constant for twin primes can be defined for cousin primes, called Brun's constant for cousin primes, with the initial term (3, 7) omitted, bu the convergent sum: :$B\_4\; =\; \backslash left(\backslash frac\; +\; \backslash frac\backslash right)\; +\; \backslash left(\backslash frac\; +\; \backslash frac\backslash right)\; +\; \backslash left(\backslash frac\; +\; \backslash frac\backslash right)\; +\; \backslash cdots.$ Using cousin primes up to 242, the value of ''B''4 was estimated by Marek Wolf in 1996 as :''B''4 ≈ 1.1970449.〔Marek Wolf, (''On the Twin and Cousin Primes'' ) (PostScript file).〕 This constant should not be confused with Brun's constant for prime quadruplets, which is also denoted ''B''4. 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「Cousin 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.