English Dictionary

prime number theorem

名詞

(number theory) The theorem that the number of prime numbers less than n asymptotically approaches n / ln(n) as n approaches infinity.

日本語の意味

素数定理：数論の定理で、nより小さい素数の数が、nが無限大に近づくにつれて、約 n/ln(n) に漸近的に近づくことを示す。

In our math seminar, the professor presented a new proof of the prime number theorem that emphasized elementary methods.

数学のセミナーで、教授は素数定理の新しい証明を示し、その証明は初等的な手法を強調していました。

意味（1）

(number theory) The theorem that the number of prime numbers less than n asymptotically approaches n / ln(n) as n approaches infinity.

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 𝜁'(s)/𝜁(s).

意味（2）

(number theory) Any theorem that concerns the distribution of prime numbers.

In [6], [11], abstract prime number theorems are proved under a variety of conditions.

prime number theorems （ plural ）