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In number theory, the second Hardy–Littlewood conjecture concerns the number of primes in intervals. If π(''x'') is the number of primes up to and including ''x'' then the conjecture states that :π(''x'' + ''y'') ≤ π(''x'') + π(''y'') for ''x'', ''y'' ≥ 2. This means that the number of primes from ''x'' + 1 to ''x'' + ''y'' is always less than or equal to the number of primes from 1 to ''y''. This is probably false in general as it is inconsistent with the more likely first Hardy–Littlewood conjecture on prime ''k''-tuples, but the first violation is likely to occur for very large values of ''x''. For example, an admissible ''k''-tuple 〔(【引用サイトリンク】 url=http://primes.utm.edu/glossary/page.php?sort=ktuple )〕 (or prime constellation) of 447 primes can be found in an interval of ''y'' = 3159 integers, while π(3159) = 446. If the first Hardy–Littlewood conjecture holds, then the first such ''k''-tuple is expected for ''x'' greater than 1.5 × 10174 but less than 2.2 × 101198.〔(【引用サイトリンク】 url=http://www.opertech.com/primes/residues.html )〕 == References == 〔 * * * * 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「Second Hardy–Littlewood conjecture」の詳細全文を読む スポンサード リンク
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