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Prime number theoremとは 意味・読み方・使い方
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意味・対訳 素数定理(そすうていり、英: Prime number theorem、独: Primzahlsatz)とは自然数の中に素数がどのくらいの「割合」で含まれているかを述べる定理である。
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In addition to that, a percentage of performing a full-scale prime number judgment method which takes time is decreased by performing the full-scale prime number judgment including Fermats small theorem, after performing trial division which is calculated at high speed beforehand, and thereby, the first and the second prime numbers p and f(p) are generated at high speed.例文帳に追加
これに加え、高速に計算可能な試行割算を先に行った後に、フェルマーの小定理を含む本格的な素数判定法を行う構成により、時間のかかる本格的な素数判定法の実行割合を減少できるので、前述した第1及び第2素数p,f(p)を高速に生成できる。 - 特許庁
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Wiktionary英語版での「Prime number theorem」の意味 |
prime number theorem
名詞
prime number theorem (複数形 prime number theorems)
- (number theory) The theorem that the number of prime numbers less than n asymptotically approaches n / ln(n) as n approaches infinity.
- 1932, A. E. Ingham, Albert Edward Ingham, The Distribution of Prime Numbers, Cambridge University Press, page 39,
- But we cannot infer from them the equivalence in any sense of these two propositions, since we have used in our proof of the prime number theorem a subsidiary theorem on the order of magnitude of .
- 1974 [Academic Press], Harold M. Edwards, Riemann's Zeta Function, 2001, Dover, page 182,
- The problem of locating the roots of , and consequently the problem of estimating the error in the prime number theorem, is closely related to the problem of estimating the growth of in the critical strip as .
- 2016, Benjamin Fine, Gerhard Rosenberger, Number Theory: An Introduction via the Density of Primes, Springer (Birkhäuser), 2nd Edition, page 145,
- In 1859, Riemann attempted to give a complete proof of the prime number theorem using the zeta function for complex variables s. Although he was not successful in proving the prime number theorem he established many properties of the zeta function and showed that the prime number theorem depended on the zeros of the zeta function.
- 1932, A. E. Ingham, Albert Edward Ingham, The Distribution of Prime Numbers, Cambridge University Press, page 39,
- (number theory) Any theorem that concerns the distribution of prime numbers.
- 1996, Illinois Journal of Mathematics, Volume 40, University of Illinois Press, page 245,
- In [6], [11], abstract prime number theorems are proved under a variety of conditions.
- 1996, Illinois Journal of Mathematics, Volume 40, University of Illinois Press, page 245,
使用する際の注意点
- The number of primes less than n may be expressed as a value of the prime-counting function, π ( n ) {\displaystyle \pi (n)} . Using asymptotic notation, the prime number theorem then becomes . A more formal expression is .
- A refinement, which actually gives closer approximations, uses the offset logarithmic integral function (Li): .
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