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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 Schinzel's hypothesis H ： ウィキペディア英語版 Schinzel's hypothesis H In mathematics, Schinzel's hypothesis H is a very broad generalisation of conjectures such as the twin prime conjecture. It aims to define the possible scope of a conjecture of the nature that several sequences of the type :$f(n),\; g(n),\; \backslash ldots,$ with values at integers $n$ of irreducible integer-valued polynomials :$f(x),\; g(x),\; \backslash ldots,$ should be able to take on prime number values simultaneously, for integers $n$ that can be ''as large as we please''. Putting it another way, there should be infinitely many such $n$, for which each of the sequence values are prime numbers. Some constraints are needed on the polynomials. Andrzej Schinzel's hypothesis builds on the earlier Bunyakovsky conjecture, for a single polynomial, and on the Hardy–Littlewood conjectures for multiple linear polynomials. It is in turn extended by the Bateman–Horn conjecture. ==Necessary limitations== Such a conjecture must be subject to some necessary conditions. For example if we take the two polynomials $x\; +\; 4$ and $x\; +\; 7$, there is no $n\; >\; 0$ for which $n\; +\; 4$ and $n\; +\; 7$ are both primes. That is because one will be an even number $n\; >\; 2$, and the other an odd number. The main question in formulating the conjecture is to rule out this phenomenon. Thus, we should add a condition: "For every prime ''p'', there is a ''n'' such that all the polynomial values at ''n'' are not divisible by ''p''". 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「Schinzel's hypothesis H」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.