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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 Sieve of Sundaram ： ウィキペディア英語版 Sieve of Sundaram In mathematics, the sieve of Sundaram is a simple deterministic algorithm for finding all prime numbers up to a specified integer. It was discovered by Indian mathematician S. P. Sundaram in 1934. ==Algorithm== Start with a list of the integers from 1 to ''n''. From this list, remove all numbers of the form ''i'' + ''j'' + 2''ij'' where: *$i,j\backslash in\backslash mathbb,\backslash \; 1\; \backslash le\; i\; \backslash le\; j$ *$i\; +\; j\; +\; 2ij\; \backslash le\; n$ The remaining numbers are doubled and incremented by one, giving a list of the odd prime numbers (i.e., all primes except 2) below 2''n'' + 2. The sieve of Sundaram sieves out the composite numbers just as sieve of Eratosthenes does, but even numbers are not considered; the work of "crossing out" the multiples of 2 is done by the final double-and-increment step. Whenever Eratosthenes' method would cross out ''k'' different multiples of a prime ''2i+1'', Sundaram's method crosses out ''i + j(2i+1)'' for $1\backslash le\; j\backslash le\; \backslash lfloor\; k/2\backslash rfloor$. 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「Sieve of Sundaram」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.